{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "FINAL Template_for CIS521_midterm notes.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "brNDGX-kvzds"
      },
      "source": [
        "# Template for Notes for CIS 521 Midterm 1\n",
        "\n",
        "The midterm exam for CIS 521 will be **open notes**. No other matierals are allowed for the exam - you may not use the textbook, the internet, a Python envionement, or communicate with anyone during the exam. \n",
        "\n",
        "This python notebook is where you should save all of your notes.  It provides a structured template that allows you to add summaries for each of the textbook sections that are part of the required reading, plus room for lecture notes and definitions.\n",
        "\n",
        "Your summaries must be written in your own words.  Do not copy and paste from the textbook.  Do not share your notes with classmates, or copy any of your classmates' notes.  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aPtM8g7R0Pds"
      },
      "source": [
        "# Instructions\n",
        "\n",
        "1. Make a copy of this Google Colab file. From the colab menu, pick **File > Save a copy in Drive**.  That will save a copy of this notebook in your Google drive.\n",
        "2. Go through each section of the notebook, and fill in all the summaries for each chapter and its corresponding sections.  Be sure to save your work frequently!\n",
        "3. Read the notes below about how you can format your summaries.\n",
        "4. In addition to these notes, you are allowed 1 page (both sides) for figures or handwritten notes.\n",
        "5. Submit your version of this notebook to Gradescope before you start the exam.\n",
        "6. If you are taking the exam in person, then you must print a copy of your notes for yourself.   Here's how to print: \n",
        "* Run the last cell of this notebook\n",
        "* Click the \"Mirror cell in tab\" button (this is located in the upper right corner of the cell, immediately to the right of the trash can).  This will open the cell.  \n",
        "* In Chrome, you can then print your notes using the **File > Print** option from the browser's menu.  \n",
        "* In the print options, change the layout from Landscape to Portrait. \n",
        "* Clicking the Save, will save a PDF that you can then print.\n",
        "\n",
        "## Formatting Notes\n",
        "\n",
        "1. The max length for each section's summary is 500 words / 3000 characters.\n",
        "2. You can also write a 2000 word summary of the lectures for each module.\n",
        "3. You may also write definitions of concepts for each module.  The definitions should be written in your own words (not copy and pasted), and they should be no more than 20 words long for each concept. \n",
        "2. You can use Markdown formatting for your summaries. \n",
        "3. You can use Latex formatting for equations. Put two dollar signs before and after your equation like this: \n",
        "$$ \\epsilon = \\frac{1}{mc^2} $$\n",
        "4. When you write python code or psuedocode algorithms, you should surround it with triple backticks like this:\n",
        "```\n",
        "def function():\n",
        "      print('hello world')\n",
        "```\n",
        "5. Write \\ whenever you want to keep writing on the next line without a newline being inserted."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cw5IpDLCZa4W"
      },
      "source": [
        "## Example summary\n",
        "\n",
        "This is a sample summary of [Section 2.1.1](https://web.stanford.edu/~jurafsky/slp3/2.pdf ) of Jurfasky and Martin's Speech and Language Processing's book\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lzaavW96tcxM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "df661bca-7fe3-4d8f-ec2f-f8def0e5c410"
      },
      "source": [
        "chapter_2_1_example = \"\"\"\n",
        "Regular expressions are an algebraic notation for characterizing \\\n",
        "a set of strings that are useful for searching for a pattern or through a corpus.\\\n",
        "Only the first matching result will be shown. The search string is case sensitive, \\\n",
        "but it can consist of a single character or a sequence of characters. \\\n",
        "While square braces specify a disjunction of characters, the dash can more easily look \\\n",
        "for characters over a range. The caret specifies the non-existence of a character. \\\n",
        "Additionally, the (?) is used to for flexibility on a single character, meaning \\\n",
        "\"the preceding character or nothing\". More importantly, the Kleene star means zero or \\\n",
        "more occurrences of the immediately previous character or regular expression in square braces.\\\n",
        "...\n",
        "\"\"\"\n",
        "\n",
        "length = len(chapter_2_1_example.split(\" \"))\n",
        "print(\"The example summary is {len} words long, so you could write an additional \\\n",
        "{remaining} words.\".format(len=length, remaining=(500-length)))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The example summary is 116 words long, so you could write an additional 384 words.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s3Uk9gQTevcj"
      },
      "source": [
        "## Example summary length\n",
        "\n",
        "The maximum summary length for each section is 500 words / 3000 characters.  Hopefully you'll find that to be quite generous. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8DvZ57A-djo1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "221148d0-f90d-40d9-9861-3108adefc4af"
      },
      "source": [
        "# This is an example of a 500 word placeholder\n",
        "placeholder = \"\"\"ultrices vitae auctor eu augue ut lectus arcu bibendum at varius \\\n",
        " vel pharetra vel turpis nunc eget lorem dolor sed viverra ipsum nunc aliquet \\\n",
        " bibendum enim facilisis gravida neque convallis a cras semper auctor neque vitae \\\n",
        " tempus quam pellentesque nec nam aliquam sem et tortor consequat id porta nibh \\\n",
        " venenatis cras sed felis eget velit aliquet sagittis id consectetur purus ut \\\n",
        " faucibus pulvinar elementum integer enim neque volutpat ac tincidunt vitae semper \\ \n",
        " quis lectus nulla at volutpat diam ut venenatis tellus in metus vulputate eu \\\n",
        " scelerisque felis imperdiet proin fermentum leo vel orci porta non pulvinar neque \\ \n",
        " laoreet suspendisse interdum consectetur libero id faucibus nisl tincidunt eget \\\n",
        " nullam non nisi est sit amet facilisis magna etiam tempor orci eu lobortis \\\n",
        " elementum nibh tellus molestie nunc non blandit massa enim nec dui nunc mattis \\\n",
        " enim ut tellus elementum sagittis vitae et leo duis ut diam quam nulla porttitor \\\n",
        " massa id neque aliquam vestibulum morbi blandit cursus risus at ultrices mi tempus \\\n",
        " imperdiet nulla malesuada pellentesque elit eget gravida cum sociis natoque \\\n",
        " penatibus et magnis dis parturient montes nascetur ridiculus mus mauris vitae \\\n",
        " ultricies leo integer malesuada nunc vel risus commodo viverra maecenas accumsan \\\n",
        " lacus vel facilisis volutpat est velit egestas dui id ornare arcu odio ut sem nulla \\\n",
        " pharetra diam sit amet nisl suscipit adipiscing bibendum est ultricies integer \\\n",
        " quis auctor elit sed vulputate mi sit amet mauris commodo quis imperdiet massa \\\n",
        " tincidunt nunc pulvinar sapien et ligula ullamcorper malesuada proin libero nunc \\\n",
        " consequat interdum varius sit amet mattis vulputate enim nulla aliquet porttitor \\\n",
        " lacus luctus accumsan tortor posuere ac ut consequat semper viverra nam libero \\\n",
        " justo laoreet sit amet cursus sit amet dictum sit amet justo donec enim diam \\\n",
        " vulputate ut pharetra sit amet aliquam id diam maecenas ultricies mi eget mauris \\\n",
        " pharetra et ultrices neque ornare aenean euismod elementum nisi quis eleifend quam \\\n",
        " adipiscing vitae proin sagittis nisl rhoncus mattis rhoncus urna neque viverra justo \\\n",
        " nec ultrices dui sapien eget mi proin sed libero enim sed faucibus turpis in \\\n",
        " eu mi bibendum neque egestas congue quisque egestas diam in arcu cursus euismod \\\n",
        " quis viverra nibh cras pulvinar mattis nunc sed blandit libero volutpat sed cras \\\n",
        " ornare arcu dui vivamus arcu felis bibendum ut tristique et egestas quis ipsum \\\n",
        " suspendisse ultrices gravida dictum fusce ut placerat orci nulla pellentesque \\\n",
        " dignissim enim sit amet venenatis urna cursus eget nunc scelerisque viverra mauris \\\n",
        " in aliquam sem fringilla ut morbi tincidunt augue interdum velit euismod in \\\n",
        " pellentesque massa placerat duis ultricies lacus sed turpis tincidunt id aliquet \\\n",
        " risus feugiat in ante metus dictum at tempor commodo ullamcorper a lacus vestibulum \\\n",
        " sed arcu non odio euismod lacinia at quis risus sed vulputate odio ut enim blandit \\\n",
        " volutpat maecenas volutpat blandit aliquam etiam erat velit scelerisque in \\\n",
        " dictum non consectetur a erat nam at lectus urna\"\"\"\n",
        "\n",
        "print(\"The length in words is\", len(placeholder.split(' ')))\n",
        "print(\"The length in characters is\", len(placeholder))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The length in words is 500\n",
            "The length in characters is 3030\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5yG3-YncJfTB"
      },
      "source": [
        "# Permissions to use your summaries\n",
        "\n",
        "We'd like to use your summaries to help develop better educational resources like [remember.school](https://remember.school) or a question-answering system about the textbook.  \n",
        "\n",
        "1. Please enter your name.  \n",
        "\n",
        "2. If you grant permission for us to use your summaries under a [Creative Commons License](https://creativecommons.org/licenses/by/4.0/), please set ```permission = True```.  If you do not grant permission, please set it to false. Your answer won't affect your grade.\n",
        "\n",
        "3. If you grant us permission, and you'd like to remain anonymous, set ```anonymous = True```.  We'll remove your name before sharing your summaries with anyone. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2RECnJArJew4"
      },
      "source": [
        "name = \"\"\n",
        "permission = True\n",
        "anonymous = False"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GZZXyrV-xuAp"
      },
      "source": [
        "# Module 1 - Intro to AI"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y2NfE1CKxzS-"
      },
      "source": [
        "# Russell and Norvig, AIMA 4th Edition, Chapter 1 “Introduction”, Section 1.1 “What is AI”\n",
        "\n",
        "chapter1_1 = \"\"\"formal definition of intelligence called rationality—loosely speaking, doing the “right thing\" \\n\n",
        "some consider intelligence to be a property of internal thought processes and reasoning, while others focus on intelligent behavior, an external characterization \\n\n",
        "capabilities for turing test: natural language processing, knowledge representation, automated reasoning, machine learning, computer vision, robotics \\n\n",
        "learn about human thought: introspection, psychological experiments, brain imaging \\n\n",
        "An agent is just something that acts \\n\n",
        "An agent is anything that perceives its environment through sensors and can act on its environment through actuators \\n\n",
        "A percept is the agent’s perceptual inputs at any given instance. \\n\n",
        "The agent program runs on the physical architecture to produce f \\n\n",
        "agent = architecture + program \\n\n",
        "a rational agent selects an action a to maximize its performance measure \\n\n",
        "A rational agent is one that acts so as to achieve the best outcome or, when there is uncertainty, the best expected outcome. \\n\n",
        "PEAS: to specify a task environment: Performance measure, Environment, Actuators, Sensors \\n\n",
        "rational-agent vs laws of thought: more general--correct inference is just one of possible mechanisms. \\n\n",
        "more amenable to scientific development \\n\n",
        "AI has focused on the study and construction of agents that do the right thing(defined by human). standard model \\n\n",
        "Construct agent FUNCTION f that maximizes the expected value of the performance measure, \\n\n",
        "Design an agent PROGRAM that implements f on a particular architecture \\n\n",
        "search problem: goal, search problem: States, Actions, Performance measure. solution \\n\n",
        "\"\"\"\n",
        "# Russell and Norvig, AIMA 4th Edition, Chapter 27 “Philosophical Foundations”, Sections 27.1 “The Limits of AI” and 27.2 “Can Machines Really Think?”\n",
        "chapter27_1 = \"\"\"\"\"\"\n",
        "chapter27_2 = \"\"\"\"\"\"\n",
        "\n",
        "# Russell and Norvig, AIMA 4th Edition, Chapter 2 “Intelligent Agents” (whole chapter)\n",
        "chapter2_1 = \"\"\"\"\"\"\n",
        "chapter2_2 = \"\"\"\"\"\"\n",
        "chapter2_3 = \"\"\"\"\"\"\n",
        "chapter2_4 = \"\"\"\"\"\"\n",
        "\n",
        "# Lecture notes \n",
        "module1_lecture_notes = \"\"\"\"\"\"\n",
        "\n",
        "\n",
        "# Definitions of concepts from Module 1.\n",
        "# You can define any bolded term in the textbook, \n",
        "# but you most use your own words for the definitions.\n",
        "# Each definition should be at most 20 words long.\n",
        "module1_definitions = {\n",
        "\"agent\" : \"anything that can perceive and act in an environment\",\n",
        "\"percept\" : \"inputs from agents' sensors\",\n",
        "\"other concept\" : \"your definitions here\",\n",
        "\"etc.\": \"your definitions here\",\n",
        "}\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "elCCgY64spuq"
      },
      "source": [
        "## Preview of your notes for Module 1\n",
        "\n",
        "Here's a preview of your how your notes will be displayed.  At the end of this Python notebook, we'll aggregate your notes for all modules together into a single display.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gYYeNcdM_maE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 955
        },
        "cellView": "form",
        "outputId": "1c423945-6410-4471-bb9c-2ada78280a8b"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "from IPython.display import display, Markdown, Latex\n",
        "\n",
        "module1_sections = [\n",
        "  (\"AIMA Chapter 1.1 What is AI?\", chapter1_1),\n",
        "  (\"AIMA Chapter 27.1 The Limits of AI\", chapter27_1),\n",
        "  (\"AIMA Chapter 27.1 Can Machines Really Think?\", chapter27_2),\n",
        "  (\"AIMA 2.1 Agents and Environments\", chapter2_1),\n",
        "  (\"AIMA 2.2 Good Behavior: The Concept of Rationality\", chapter2_2),\n",
        "  (\"AIMA 2.3 The Nature of Environments\", chapter2_3),\n",
        "  (\"AIMA 2.4 The Structure of Agents\", chapter2_4),\n",
        "  (\"Module 1 Lecture Notes\", module1_lecture_notes),\n",
        "]\n",
        "\n",
        "\n",
        "def length_check(sections):\n",
        "  warnings = \"\"\n",
        "  for section, summary in sections:\n",
        "    max_word_length = 500\n",
        "    max_character_length = 3000\n",
        "    if \"lecture\" in section.lower():\n",
        "      # It's OK to do longer summaries of the lectures\n",
        "      max_word_length = 2000\n",
        "      max_character_length = 12000  \n",
        "    if (len(summary) > max_character_length or len(summary.split(' ')) > max_word_length):\n",
        "      warnings += \"WARNING: Your summary of '{section}' is too long!\\n\".format(section=section)\n",
        "  return warnings\n",
        "\n",
        "def length_check_definitions(definitions):\n",
        "  warnings = \"\"\n",
        "  for concept, definition in definitions.items():\n",
        "    if(len(definition.split(' ')) > 20):\n",
        "      warnings += \"WARNING: Your definition of '{concept}' is too long!\\n\".format(concept=concept)\n",
        "  return warnings\n",
        "\n",
        "\n",
        "def format_module(module_num, title, sections, definitions, show_placeholder=False):\n",
        "  markdown = \"\"\n",
        "\n",
        "  # Check summary lengths\n",
        "  warnings = length_check(sections)\n",
        "  if warnings != \"\":\n",
        "    markdown += \"## \" + warnings\n",
        "\n",
        "  # Check definition lengths\n",
        "  warnings = length_check_definitions(definitions)\n",
        "  if warnings != \"\":\n",
        "    markdown += \"## \" + warnings\n",
        "\n",
        "  markdown += \"# Module {num}: {title}\\n\".format(num=module_num, title=title)\n",
        "\n",
        "\n",
        "  for section, summary in sections:\n",
        "    if show_placeholder and summary == \"\":\n",
        "      summary = placeholder\n",
        "    markdown += \"## {section}\\n{summary}\\n\\n\".format(section=section, summary=summary)\n",
        "  \n",
        "  markdown += \"## Module {num} Definitions\\n\".format(num=module_num)\n",
        "  for concept, definition in definitions.items():\n",
        "    markdown += \"* **{concept}** - {definition}\\n\".format(concept=concept.capitalize(), definition=definition)\n",
        "  return markdown\n",
        "\n",
        "\n",
        "module1_markdown = format_module(1, \"Rational Agents and Task Environments\", module1_sections, module1_definitions)\n",
        "display(Markdown(module1_markdown))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 1: Rational Agents and Task Environments\n## AIMA Chapter 1.1 What is AI?\nformal definition of intelligence called rationality—loosely speaking, doing the “right thing\" \n\nsome consider intelligence to be a property of internal thought processes and reasoning, while others focus on intelligent behavior, an external characterization \n\ncapabilities for turing test: natural language processing, knowledge representation, automated reasoning, machine learning, computer vision, robotics \n\nlearn about human thought: introspection, psychological experiments, brain imaging \n\nAn agent is just something that acts \n\nAn agent is anything that perceives its environment through sensors and can act on its environment through actuators \n\nA percept is the agent’s perceptual inputs at any given instance. \n\nThe agent program runs on the physical architecture to produce f \n\nagent = architecture + program \n\na rational agent selects an action a to maximize its performance measure \n\nA rational agent is one that acts so as to achieve the best outcome or, when there is uncertainty, the best expected outcome. \n\nPEAS: to specify a task environment: Performance measure, Environment, Actuators, Sensors \n\nrational-agent vs laws of thought: more general--correct inference is just one of possible mechanisms. \n\nmore amenable to scientific development \n\nAI has focused on the study and construction of agents that do the right thing(defined by human). standard model \n\nConstruct agent FUNCTION f that maximizes the expected value of the performance measure, \n\nDesign an agent PROGRAM that implements f on a particular architecture \n\nsearch problem: goal, search problem: States, Actions, Performance measure. solution \n\n\n\n## AIMA Chapter 27.1 The Limits of AI\n\n\n## AIMA Chapter 27.1 Can Machines Really Think?\n\n\n## AIMA 2.1 Agents and Environments\n\n\n## AIMA 2.2 Good Behavior: The Concept of Rationality\n\n\n## AIMA 2.3 The Nature of Environments\n\n\n## AIMA 2.4 The Structure of Agents\n\n\n## Module 1 Lecture Notes\n\n\n## Module 1 Definitions\n* **Agent** - anything that can perceive and act in an environment\n* **Percept** - inputs from agents' sensors\n* **Other concept** - your definitions here\n* **Etc.** - your definitions here\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9xRbdqDox2zD"
      },
      "source": [
        "#Module 2 - Python"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DpBvu7EMx7sy"
      },
      "source": [
        "# No readings for this module.  Instead you can summarize the lecture instead.\n",
        "\n",
        "# Lecture notes \n",
        "module2_lecture_notes = \"\"\" Python: dynamic typing Drawback: type errors are only caught at runtime \\n\n",
        "Immutable: string, tuple \\n\n",
        "mutable: list \\n\n",
        "key of the dinctionary must be immutable \\n\n",
        "comprehension: newlist = [x for x in fruits if \"a\" in x] \\n\n",
        "newlist = [x if x != \"banana\" else \"orange\" for x in fruits] \\n\n",
        "\n",
        "\"\"\"\n",
        "\n",
        "# Each definition should be at most 20 words long.\n",
        "module2_definitions = {\n",
        "\"mutability\" : \"your definition here\",\n",
        "}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ydOK__lwWgdp",
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 324
        },
        "outputId": "0025fdbd-f4f9-4288-a50d-49fc0f938d8f"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "\n",
        "module2_sections = [\n",
        "  (\"Module 2 Lecture Notes\", module2_lecture_notes),\n",
        "]\n",
        "\n",
        "module2_markdown = format_module(2, \"Python\", module2_sections, module2_definitions)\n",
        "display(Markdown(module2_markdown))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 2: Python\n## Module 2 Lecture Notes\n Python: dynamic typing Drawback: type errors are only caught at runtime \n\nImmutable: string, tuple \n\nmutable: list \n\nkey of the dinctionary must be immutable \n\ncomprehension: newlist = [x for x in fruits if \"a\" in x] \n\nnewlist = [x if x != \"banana\" else \"orange\" for x in fruits] \n\n\n\n\n## Module 2 Definitions\n* **Mutability** - your definition here\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "46MQLR-Gx8dZ"
      },
      "source": [
        "#Module 3 - Search Problems"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BN0b1eVYx-nd"
      },
      "source": [
        "# Russell and Norvig, AIMA 4th Edition, AIMA Chapter 3 “Problem Solving by Search” (3.1-3.4)\n",
        "chapter3_1 = \"\"\"\"\"\"\n",
        "chapter3_2 = \"\"\"\"\"\"\n",
        "chapter3_3 = \"\"\"\"\"\"\n",
        "chapter3_4 = \"\"\"\"\"\"\n",
        "\n",
        "\n",
        "# Lecture notes \n",
        "module3_lecture_notes = \"\"\"Fully observable=Deterministic=Known environment \\n\n",
        "Partially observable or Nondeterministic \\n\n",
        "Definition: States, initial state, Actions, Transition Model, Path cost, Goal test \\n\n",
        "Tree Search: Enumerate in some order all possible paths from the initial state. Search through explicit tree generation \\n\n",
        "Nodes in search tree generated through transition model \\n\n",
        "The EXPAND function uses the Actions and Transition Model to create the corresponding states: creates new nodes, fills in the various fields \\n\n",
        "Tree search Problem: Failure to detect repeated states can turn a linear problem into an exponential one! \\n\n",
        "solution: Graph Search: must keep track of all possible states (can use a lot of memory) \\n\n",
        "Uninformed search: AKA “Blind search” Uses only information available in problem definition \\n\n",
        "Strategy = order of tree expansion \\n\n",
        "Completeness- always find the solution? \\n\n",
        "Optimality - finds a least cost solution (lowest path cost) first? \\n\n",
        "BFS: frontier is FIFO (First-In-First-Out) Queue. Complete? Yes (if b is finite) Optimal? Yes\\n\n",
        "Time Complexity: O(b^d) Space: O(b^d) \\n\n",
        "DFS: frontier is LIFO (Last-In-First-Out) Queue \\n\n",
        "Complete? No. It fails in infinite-depth spaces, spaces with loops \\n\n",
        "If we modify it to avoid repeated states along path, then it is complete in finite spaces. Optimal? No \\n\n",
        "time: O(b^m) Space: O(bm)  m:max depth \\n\n",
        "Depth-limited search: Depth-First search but with depth limit l. If l < d then incomplete. If l > d then not optimal \\n\n",
        "Time: O(b^l), space: O(bl) \\n\n",
        "Iterative deepening search: Complete & optimal. Time: O(b^d), Space: O(bd) \\n\n",
        "\"\"\"\n",
        "\n",
        "# Definitions of concepts from Module 3.\n",
        "# You can define any bolded term in the textbook, \n",
        "# but you most use your own words for the definitions.\n",
        "# Each definition should be at most 20 words long.\n",
        "module3_definitions = {\n",
        "\"problem-solving agent\" : \"an agent that can formulate a plan via search\", \n",
        "\"Reflex Agents\" : \"one that selects an action based only on the current percept and ignores the rest of the percept history\",\n",
        "\"search\" : \"the computational process that it undertakes.\",\n",
        "\"solution\" : \"The sequence that agent will consider actions that form a path to a goal state.\",\n",
        "\"State space\": \"the set of all states reachable from the initial state by any sequence of actions\",\n",
        "\"Path\": \"a sequence of actions leading from one state sj to another state sk\",\n",
        "\"Solution\": \"a path from the initial state si to a state sf that satisfies the goal test\",\n",
        "\"Search tree\": \"a way of representing the paths that a search algorithm has explored.\",\n",
        "\"Frontier\": \"those states that are available for expanding\",\n",
        "\"Optimal Solution\": \"A solution is optimal if no solution has a lower path cost.\",\n",
        "}\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lvtN3p7ET3Tx",
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 995
        },
        "outputId": "6fe8d241-f949-4fef-c961-d2f6c08dc3b5"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module3_sections = [\n",
        "  (\"AIMA Chapter 3.1 Problem-Solving Agents\", chapter3_1),\n",
        "  (\"AIMA Chapter 3.2 Example Problems\", chapter3_2),\n",
        "  (\"AIMA Chapter 3.3 Search Algorithms\", chapter3_3),\n",
        "  (\"AIMA Chapter 3.4 Uninformed Search Strategies\", chapter3_4),\n",
        "  (\"Module 3 Lecture Notes\", module3_lecture_notes),\n",
        "]\n",
        "\n",
        "module3_markdown = format_module(3, \"Search Problems\", module3_sections, module3_definitions)\n",
        "display(Markdown(module3_markdown))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 3: Search Problems\n## AIMA Chapter 3.1 Problem-Solving Agents\n\n\n## AIMA Chapter 3.2 Example Problems\n\n\n## AIMA Chapter 3.3 Search Algorithms\n\n\n## AIMA Chapter 3.4 Uninformed Search Strategies\n\n\n## Module 3 Lecture Notes\nFully observable=Deterministic=Known environment \n\nPartially observable or Nondeterministic \n\nDefinition: States, initial state, Actions, Transition Model, Path cost, Goal test \n\nTree Search: Enumerate in some order all possible paths from the initial state. Search through explicit tree generation \n\nNodes in search tree generated through transition model \n\nThe EXPAND function uses the Actions and Transition Model to create the corresponding states: creates new nodes, fills in the various fields \n\nTree search Problem: Failure to detect repeated states can turn a linear problem into an exponential one! \n\nsolution: Graph Search: must keep track of all possible states (can use a lot of memory) \n\nUninformed search: AKA “Blind search” Uses only information available in problem definition \n\nStrategy = order of tree expansion \n\nCompleteness- always find the solution? \n\nOptimality - finds a least cost solution (lowest path cost) first? \n\nBFS: frontier is FIFO (First-In-First-Out) Queue. Complete? Yes (if b is finite) Optimal? Yes\n\nTime Complexity: O(b^d) Space: O(b^d) \n\nDFS: frontier is LIFO (Last-In-First-Out) Queue \n\nComplete? No. It fails in infinite-depth spaces, spaces with loops \n\nIf we modify it to avoid repeated states along path, then it is complete in finite spaces. Optimal? No \n\ntime: O(b^m) Space: O(bm)  m:max depth \n\nDepth-limited search: Depth-First search but with depth limit l. If l < d then incomplete. If l > d then not optimal \n\nTime: O(b^l), space: O(bl) \n\nIterative deepening search: Complete & optimal. Time: O(b^d), Space: O(bd) \n\n\n\n## Module 3 Definitions\n* **Problem-solving agent** - an agent that can formulate a plan via search\n* **Reflex agents** - one that selects an action based only on the current percept and ignores the rest of the percept history\n* **Search** - the computational process that it undertakes.\n* **Solution** - The sequence that agent will consider actions that form a path to a goal state.\n* **State space** - the set of all states reachable from the initial state by any sequence of actions\n* **Path** - a sequence of actions leading from one state sj to another state sk\n* **Solution** - a path from the initial state si to a state sf that satisfies the goal test\n* **Search tree** - a way of representing the paths that a search algorithm has explored.\n* **Frontier** - those states that are available for expanding\n* **Optimal solution** - A solution is optimal if no solution has a lower path cost.\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WHREsHSSyA-h"
      },
      "source": [
        "#Module 4 - Informed Search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tuFC8w7CyCns"
      },
      "source": [
        "# Russell and Norvig, AIMA Chapter 3 “Problem Solving by Search” (3.5-3.6)\n",
        "chapter3_5 = \"\"\"\"\"\"\n",
        "chapter3_6 = \"\"\"\"\"\"\n",
        "\n",
        "\n",
        "# Lecture notes \n",
        "module4_lecture_notes = \"\"\"\n",
        "An informed search strategy uses domain-specific information about the location of the goals in order to find a solution more efficiently than uninformed search. \\n\n",
        "uniform-cost search (UCS): step cost=1. \\n\n",
        "Difference with BFS: Tests if a node is a goal state when it is selected for expansion, not when it is added to the frontier \\n\n",
        "Best-first search: node selected for expansion based on an evaluation function f(n) (includes estimate of distance to goal) \\n\n",
        "A heuristic function h(n) takes a state n and returns an estimate of the distance from n to the goal. \\n\n",
        "Greedy best-first search: f(n) = h(n) Completely ignores g(n): the cost to get to n \\n\n",
        "not optimal, not complete can get stuck in loops \\n\n",
        "A* search: Key Idea: avoid expanding paths that are already expensive, but expand most promising first. f(n)=g(n) + h(n) \\n\n",
        "A heuristic h(n) is admissible/optimistic if it never overestimates the cost to reach the goal;  \\n\n",
        "Inadmissible (pessimistic) heuristics: break optimality by pushing good plans too far back on the frontier, which means they may never get expanded. \\n\n",
        "If h(n) is admissible, A* using Tree Search is optimal \\n\n",
        "Relaxed problems: A problem with fewer restrictions on the actions than the original \\n\n",
        "The cost of an optimal solution to a relaxed problem is an admissible heuristic for the original problem \\n\n",
        "Dominance: If h2(n) ≥ h1(n) for all n (both admissible) then h2 dominates h1 \\n\n",
        "\"\"\"\n",
        "\n",
        "# Definitions\n",
        "module4_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vqtEs0gHs9sO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 594
        },
        "cellView": "form",
        "outputId": "feaf9ebe-0be1-40bd-edfd-da867ef168ec"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module4_sections = [\n",
        "  (\"AIMA Chapter 3.5 Informed (Heuristic) Search Strategies\", chapter3_5),\n",
        "  (\"AIMA Chapter 3.6 Heuristic Functions\", chapter3_6),\n",
        "  (\"Module 4 Lecture Notes\", module4_lecture_notes),\n",
        "]\n",
        "\n",
        "module4_markdown = format_module(4, \"Informed Search\", \n",
        "                         module4_sections, \n",
        "                         module4_definitions)\n",
        "display(Markdown(module4_markdown))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 4: Informed Search\n## AIMA Chapter 3.5 Informed (Heuristic) Search Strategies\n\n\n## AIMA Chapter 3.6 Heuristic Functions\n\n\n## Module 4 Lecture Notes\n\nAn informed search strategy uses domain-specific information about the location of the goals in order to find a solution more efficiently than uninformed search. \n\nuniform-cost search (UCS): step cost=1. \n\nDifference with BFS: Tests if a node is a goal state when it is selected for expansion, not when it is added to the frontier \n\nBest-first search: node selected for expansion based on an evaluation function f(n) (includes estimate of distance to goal) \n\nA heuristic function h(n) takes a state n and returns an estimate of the distance from n to the goal. \n\nGreedy best-first search: f(n) = h(n) Completely ignores g(n): the cost to get to n \n\nnot optimal, not complete can get stuck in loops \n\nA* search: Key Idea: avoid expanding paths that are already expensive, but expand most promising first. f(n)=g(n) + h(n) \n\nA heuristic h(n) is admissible/optimistic if it never overestimates the cost to reach the goal;  \n\nInadmissible (pessimistic) heuristics: break optimality by pushing good plans too far back on the frontier, which means they may never get expanded. \n\nIf h(n) is admissible, A* using Tree Search is optimal \n\nRelaxed problems: A problem with fewer restrictions on the actions than the original \n\nThe cost of an optimal solution to a relaxed problem is an admissible heuristic for the original problem \n\nDominance: If h2(n) ≥ h1(n) for all n (both admissible) then h2 dominates h1 \n\n\n\n## Module 4 Definitions\n* **Concept** - definition\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F3FPMzG9yUls"
      },
      "source": [
        "#Module 5 - Adversarial Search and Games"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iEIOpL7vyWcc"
      },
      "source": [
        "# Russell and Norvig, AIMA chapter 5 \"Adversarial Search\"”\" (5.1-5.3, and 5.5).\n",
        "chapter5_1 = \"\"\"\"\"\"\n",
        "chapter5_2 = \"\"\"\"\"\"\n",
        "chapter5_3 = \"\"\"\"\"\"\n",
        "chapter5_5 = \"\"\"\"\"\"\n",
        "\n",
        "# Russell and Norvig, AIMA Chapter 16 “Making Simple Decisions” (16.1-16.3)\n",
        "chapter16_1 = \"\"\"\"\"\"\n",
        "chapter16_2 = \"\"\"\"\"\"\n",
        "chapter16_3 = \"\"\"\"\"\"\n",
        "\n",
        "# Lecture notes \n",
        "module5_lecture_notes = \"\"\" \n",
        "fully observable = perfect information \\n\n",
        "Strategic: The next state is determined by the current state and the action executed by the agent and the actions of one other agent. \\n\n",
        "Zero-sum: one player’s loss is another’s gain \\n\n",
        "Games as search: Initial state, Successor function, Terminal test, Utility function \\n\n",
        "Evaluation functions: f(n) Evaluates how good a ‘board position’ is \\n\n",
        "minimax value: the best achievable utility against a rational (optimal) adversary \\n\n",
        "Alpha-Beta Pruning: α: MAX’s current lower bound on MAX’s outcome \\n\n",
        "β: MIN’s current upper bound on MIN’s outcome \\n\n",
        "When evaluating a MAX node: a value v ≥ β is backed-up. MIN will never select that MAX node \\n\n",
        "When evaluating a MIN node: a value v ≤ α is found. MAX will never select that MIN node \\n\n",
        "Expectimax search: compute the average score under optimal play \\n\n",
        "Objectivist / frequentist answer: Averages over repeated experiments \\n\n",
        "Subjectivist / Bayesian answer: Degrees of belief about unobserved variables \\n\n",
        "\"\"\"\n",
        "\n",
        "# Definitions\n",
        "module5_definitions = {\n",
        "\"concept\" : \"definition\",    \n",
        "}\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "KUc_LgzDvWf-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 789
        },
        "outputId": "66738313-2a0a-45b3-cb1d-13f07d3a396f"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module5_sections = [\n",
        "  (\"AIMA Chapter 5.1 Game Theory\", chapter5_1),\n",
        "  (\"AIMA Chapter 5.2 Optimal Decisions in Games\", chapter5_2),\n",
        "  (\"AIMA Chapter 5.3 Heuristic Alpha–Beta Tree Search\", chapter5_3),\n",
        "  (\"AIMA Chapter 5.5 Stochastic Games\", chapter5_5),\n",
        "  (\"AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\", chapter16_1),\n",
        "  (\"AIMA Chapter 16.2 The Basis of Utility Theory\", chapter16_2),\n",
        "  (\"AIMA Chapter 16.3 Utility Functions\", chapter16_3),\n",
        "  (\"Module 5 Lecture Notes\", module5_lecture_notes),\n",
        "]\n",
        "\n",
        "module5_markdown = format_module(5, \"Adversarial Search and Games\", \n",
        "                         module5_sections, \n",
        "                         module5_definitions)\n",
        "display(Markdown(module5_markdown))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 5: Adversarial Search and Games\n## AIMA Chapter 5.1 Game Theory\n\n\n## AIMA Chapter 5.2 Optimal Decisions in Games\n\n\n## AIMA Chapter 5.3 Heuristic Alpha–Beta Tree Search\n\n\n## AIMA Chapter 5.5 Stochastic Games\n\n\n## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n\n\n## AIMA Chapter 16.2 The Basis of Utility Theory\n\n\n## AIMA Chapter 16.3 Utility Functions\n\n\n## Module 5 Lecture Notes\n \nfully observable = perfect information \n\nStrategic: The next state is determined by the current state and the action executed by the agent and the actions of one other agent. \n\nZero-sum: one player’s loss is another’s gain \n\nGames as search: Initial state, Successor function, Terminal test, Utility function \n\nEvaluation functions: f(n) Evaluates how good a ‘board position’ is \n\nminimax value: the best achievable utility against a rational (optimal) adversary \n\nAlpha-Beta Pruning: α: MAX’s current lower bound on MAX’s outcome \n\nβ: MIN’s current upper bound on MIN’s outcome \n\nWhen evaluating a MAX node: a value v ≥ β is backed-up. MIN will never select that MAX node \n\nWhen evaluating a MIN node: a value v ≤ α is found. MAX will never select that MIN node \n\nExpectimax search: compute the average score under optimal play \n\nObjectivist / frequentist answer: Averages over repeated experiments \n\nSubjectivist / Bayesian answer: Degrees of belief about unobserved variables \n\n\n\n## Module 5 Definitions\n* **Concept** - definition\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qVSQhTVSyYYO"
      },
      "source": [
        "#Module 6 - \"Constraint Satisfaction Problems\""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wm4mfW82yaRH"
      },
      "source": [
        "# Russell and Norvig, AIMA, Chapter 6 “Constraint Satisfaction Problems” (6.1-6.5)\n",
        "chapter6_1 = \"\"\"\"\"\"\n",
        "chapter6_2 = \"\"\"\"\"\"\n",
        "chapter6_3 = \"\"\"\"\"\"\n",
        "chapter6_4 = \"\"\"\"\"\"\n",
        "chapter6_5 = \"\"\"\"\"\"\n",
        "\n",
        "\n",
        "# Lecture notes \n",
        "module6_lecture_notes = \"\"\"Identification: assignments to variables The goal itself is important, not the path \\n\n",
        "CSPs are specialized for **identification problems** \\n\n",
        "Represent the constraints that solutions must satisfy in a uniform declarative language \\n\n",
        "Find solutions by GENERAL PURPOSE search algorithms with no changes from problem to problem \\n\n",
        "A **CSP** consists of: Finite set of variables, Nonempty domain of possible values for each variable, Finite set of constraints \\n\n",
        "A **consistent** assignment does not violate the constraints \\n\n",
        "An assignment is **complete** when every variable is assigned a value. \\n\n",
        "A solution to a CSP is a complete, consistent assignment \\n\n",
        "Constraint graph: **nodes** are variables, **arcs** are (binary) constraints \\n\n",
        "A binary CSP: each constraint relates two variables \\n\n",
        "Preference (soft constraints) can be represented by a cost for each variable assignment  \\n\n",
        "Unary constraints involve a single variable \\n\n",
        "A CSP can easily be expressed as a search problem: \\n\n",
        "**Initial State**: the empty assignment \\n\n",
        "**Successor function**: Assign value to any unassigned variable provided that there is not a constraint conflict. \\n\n",
        "**Goal test**: the current assignment is complete \\n\n",
        "**Path cost**: a constant cost for every step \\n\n",
        "variables of domain size d, Branching factor at the root is n*d \\n\n",
        "Tree has n!*d^n leaves \\n\n",
        "Depth-first search for CSPs with single-variable assignments is called **backtracking search** (uninformed algorithm for CSPs) \\n\n",
        "**General-purpose** methods & **general-purpose** heuristics can give huge gains in speed, **on average** \\n\n",
        "variable should be assigned next: 1. Most **constrained** variable(with the fewest legal values) 2. (if ties:) Most **constraining** variable (with the most constraints on remaining variables) \\n\n",
        "variable’s values be tried: Least constraining value(the one that rules out the fewest values in the remaining variables) \\n\n",
        "detect inevitable failure early: **Forward checking** (Keep track of remaining legal values for unassigned variables) \\n\n",
        "Terminate search when any unassigned variable has no remaining legal values\\n\n",
        "**Constraint propagation** goes beyond forward checking & repeatedly enforces constraints locally \\n\n",
        "CSP solvers combine search(assigning a value to a variable) and inference(Constraint propagation) \\n\n",
        "X -> Y is consistent iff for every value x of X there is some allowed y \\n\n",
        "Search: Use constraints to add labels to find one solution \\n\n",
        "Constraint Propagation: Use constraints to eliminate labels to simultaneously find all solutions \\n\n",
        "AC-3 improvements: \n",
        "1. At each iteration, we only need to examine those Xi where at least one neighbor of Xi has lost a value in the previous iteration \\n\n",
        "2. If Xi loses a value only because of arc inconsistencies with Yj , we don’t need to check Yj on the next iteration. \\n\n",
        "3. Removing a value on Xi can only make Yj arc inconsistent with respect to Xi itself. Thus, we only need to check that (j,i) is still arc-consistent.\n",
        "\"\"\" \n",
        "\n",
        "# Definitions\n",
        "module6_definitions = {\n",
        "\"Node consistency\" : \"satisfies unary constraints\",\n",
        "\"Arc consistency\":\"satisfies binary constraints\",\n",
        "\"AC-3 Time Complexity\" : \"(n^2d^3)\",\n",
        "\n",
        "}\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "kKWbCsbfxL3R",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "62eaf8ba-49cd-4fbb-eefb-3594440bb3e6"
      },
      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module6_sections = [\n",
        "  (\"AIMA Chapter 6.1 Defining Constraint Satisfaction Problems\", chapter6_1),\n",
        "  (\"AIMA Chapter 6.2 Constraint Propagation: Inference in CSPs\", chapter6_2),\n",
        "  (\"AIMA Chapter 6.3 Backtracking Search for CSPs\", chapter6_3),\n",
        "  (\"AIMA Chapter 6.4 Local Search for CSPs\", chapter6_4),\n",
        "  (\"AIMA Chapter 6.5 The Structure of Problems\", chapter6_5),\n",
        "  (\"Module 6 Lecture Notes\", module6_lecture_notes),\n",
        "]\n",
        "\n",
        "module6_markdown = format_module(6, \"Constraint Satisfaction Problems\", \n",
        "                         module6_sections, \n",
        "                         module6_definitions)\n",
        "display(Markdown(module6_markdown))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 6: Constraint Satisfaction Problems\n## AIMA Chapter 6.1 Defining Constraint Satisfaction Problems\n\n\n## AIMA Chapter 6.2 Constraint Propagation: Inference in CSPs\n\n\n## AIMA Chapter 6.3 Backtracking Search for CSPs\n\n\n## AIMA Chapter 6.4 Local Search for CSPs\n\n\n## AIMA Chapter 6.5 The Structure of Problems\n\n\n## Module 6 Lecture Notes\nIdentification: assignments to variables The goal itself is important, not the path \n\nCSPs are specialized for **identification problems** \n\nRepresent the constraints that solutions must satisfy in a uniform declarative language \n\nFind solutions by GENERAL PURPOSE search algorithms with no changes from problem to problem \n\nA **CSP** consists of: Finite set of variables, Nonempty domain of possible values for each variable, Finite set of constraints \n\nA **consistent** assignment does not violate the constraints \n\nAn assignment is **complete** when every variable is assigned a value. \n\nA solution to a CSP is a complete, consistent assignment \n\nConstraint graph: **nodes** are variables, **arcs** are (binary) constraints \n\nA binary CSP: each constraint relates two variables \n\nPreference (soft constraints) can be represented by a cost for each variable assignment  \n\nUnary constraints involve a single variable \n\nA CSP can easily be expressed as a search problem: \n\n**Initial State**: the empty assignment \n\n**Successor function**: Assign value to any unassigned variable provided that there is not a constraint conflict. \n\n**Goal test**: the current assignment is complete \n\n**Path cost**: a constant cost for every step \n\nvariables of domain size d, Branching factor at the root is n*d \n\nTree has n!*d^n leaves \n\nDepth-first search for CSPs with single-variable assignments is called **backtracking search** (uninformed algorithm for CSPs) \n\n**General-purpose** methods & **general-purpose** heuristics can give huge gains in speed, **on average** \n\nvariable should be assigned next: 1. Most **constrained** variable(with the fewest legal values) 2. (if ties:) Most **constraining** variable (with the most constraints on remaining variables) \n\nvariable’s values be tried: Least constraining value(the one that rules out the fewest values in the remaining variables) \n\ndetect inevitable failure early: **Forward checking** (Keep track of remaining legal values for unassigned variables) \n\nTerminate search when any unassigned variable has no remaining legal values\n\n**Constraint propagation** goes beyond forward checking & repeatedly enforces constraints locally \n\nCSP solvers combine search(assigning a value to a variable) and inference(Constraint propagation) \n\nX -> Y is consistent iff for every value x of X there is some allowed y \n\nSearch: Use constraints to add labels to find one solution \n\nConstraint Propagation: Use constraints to eliminate labels to simultaneously find all solutions \n\nAC-3 improvements: \n1. At each iteration, we only need to examine those Xi where at least one neighbor of Xi has lost a value in the previous iteration \n\n2. If Xi loses a value only because of arc inconsistencies with Yj , we don’t need to check Yj on the next iteration. \n\n3. Removing a value on Xi can only make Yj arc inconsistent with respect to Xi itself. Thus, we only need to check that (j,i) is still arc-consistent.\n\n\n## Module 6 Definitions\n* **Node consistency** - satisfies unary constraints\n* **Arc consistency** - satisfies binary constraints\n* **Ac-3 time complexity** - (n^2d^3)\n",
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        "id": "RYESi2kMybL8"
      },
      "source": [
        "#Module 7 - Logical Agents"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qIRJ4YYCzNHL"
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      "source": [
        "# Russell and Norvig, AIMA Chapter 7 “Logical Agents” (Sections 7.1-7.5)\n",
        "\n",
        "chapter7_1 = \"\"\"\"\"\"\n",
        "chapter7_2 = \"\"\"\"\"\"\n",
        "chapter7_3 = \"\"\"\"\"\"\n",
        "chapter7_4 = \"\"\"\"\"\"\n",
        "chapter7_5 = \"\"\"\"\"\"\n",
        "\n",
        "# Lecture notes \n",
        "module7_lecture_notes = \"\"\"\n",
        "**Knowledge-based agents** use a process of reasoning over an internal representation of knowledge to decide what action to take. \\n\n",
        "A KB contains a set of sentence that are written in a knowledge representation language. \\n\n",
        "The semantics defines the **truth** of each sentence with respect to a **possible world**, which we will often call a **model**. \\n\n",
        "If sentence α is true in model m: m satisfy α or m is a model of α \\n\n",
        "Only P True, Q False, P ⟹ Q is False. In other conditions, P ⟹ Q is True \\n\n",
        "P ⇔ Q = P⟹Q ⋀ Q⟹P \\n\n",
        "**Complex sentences** are constructed from simpler ones using **parentheses** and **logical connectives**. \\n\n",
        "α ≡ β if and only if α⊨β and β⊨α \\n\n",
        "Conjunctive Normal Form (CNF): Every sentence of propositional logic is logically equivalent to a conjunction of clauses. Clauses are disjunctions of literals. \\n\n",
        "Resolution Algorithm: To show KB⊨α then we can show that KB ⋀ ¬α is unsatisfiable. \\n\n",
        "closed under resolution: If you apply resolution to a horn clause, you get back a horn clause \\n\n",
        "¬ L1,1 ⋁ ¬ Breeze ⋁ B1,1 can be written as the implication L1,1 ⋀ Breeze ⟹ B1,1 \\n\n",
        "Forward Chaining is a kind of data-driven reasoning. \\n\n",
        "Backward chaining works backwards from a query \\n\n",
        "Backward chaining is a form of goal-directed reasoning \\n\n",
        "\"\"\"\n",
        "\n",
        "# Definitions\n",
        "module7_definitions = {\n",
        "\"Axioms\" : \"– a sentence that is given \", \n",
        "\"Derived sentences\" : \"a new sentence that is derived from others sentences\",\n",
        "\"inference\" : \"The process of deriving new sentences from old sentences\",\n",
        "\"semantics of the sentences\" : \"their meaning\",\n",
        "\"M(α)\" :\"set of all models of α\",\n",
        "\"entailment ⊨\": \"a sentence follows logically from another sentence α⊨β if and only if M(α) ⊆ M(β)\",\n",
        "\"KB ⊢i α\" : \"α is derived from KB by i\",\n",
        "\"Atomic sentences\" : \"represented with a single propositional symbols\", \n",
        "\"Propositional symbols\" : \"a statement that can be true or false\",\n",
        "\"¬(not)\" : \"negation\",\n",
        "\"⋀(and)\" : \"conjunction\",\n",
        "\"⋁(or)\" : \"disjunction\",\n",
        "\"⟹ (implies)\" : \"W⟹ S implication, W premise or antecede, S conclusion or consequence\",\n",
        "\"⇔ (if and only if)\" : \"biconditional\",\n",
        "\"Soundness\" : \"inference algorithm should only derive entailed sentences.\",\n",
        "\"Completeness\" : \"if it can derive all sentences that are entailed\",\n",
        "\"logically equivalent ≡\" : \"they are true in the same set of models\",\n",
        "\"Commutativity\" : \"(α ⋀ β) ≡ (β ⋀ α)\",\n",
        "\"Associativity\" : \"((α ⋀ β) ⋀ ɣ) ≡ (α ⋀ (β ⋀ ɣ))\",\n",
        "\"Contraposition\" : \"(α ⟹ β) ≡ (¬β ⟹ ¬α)\",\n",
        "\"Implication elimination\" : \"(α ⟹ β) ≡ (¬α ⋁ β)\",\n",
        "\"Biconditional elimination\" : \"(α ⇔ β) ≡ ((α ⟹ β) ⋀ (β ⟹α))\",\n",
        "\"De Morgan\" : \"¬(α ⋀ β) ≡ (¬α ⋁ ¬β)\",\n",
        "\"Distributivity of ⋀ over ⋁\" : \"((α ⋀ β) ⋁ ɣ) ≡ ((α ⋀ β) ⋁ (α ⋀ ɣ)))\",\n",
        "\"Distributivity of ⋁ over ⋀\" : \"((α ⋁ β) ⋀ ɣ) ≡ ((α ⋁ β) ⋀ (α ⋁ ɣ)))\",\n",
        "\"Monotonicity\" : \"if KB⊨α then KB ⋀ β ⊨α\",\n",
        "\"Eliminate ⟹\" : \"α ⟹ β with ¬α ⋁ β\",\n",
        "\"unit resolution\":\"If ℓi and m are complementary literals, then we can eliminate them\",\n",
        "\"Definite clause\" : \"disjunction of literals where exactly one is positive\",\n",
        "\"Horn clause\" : \"disjunction of literals where at most one is positive\"\n",
        "}\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
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      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "lXNcHuKjyNXa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "af6bd13b-2a52-4f36-f08e-69aea060db85"
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      "source": [
        "#@title Preview of your summary\n",
        "#@markdown You don't need to modify anything in this cell. Just press play.\n",
        "module7_sections = [\n",
        "  (\"AIMA Chapter 7.1 Knowledge-Based Agents\", chapter7_1),\n",
        "  (\"AIMA Chapter 7.2 The Wumpus World\", chapter7_2),\n",
        "  (\"AIMA Chapter 7.3 Logic\", chapter7_3),\n",
        "  (\"AIMA Chapter 7.4 Propositional Logic: A Very Simple Logic\", chapter7_4),\n",
        "  (\"AIMA 7.5 Propositional Theorem Proving\", chapter7_5),\n",
        "  (\"Module 7 Lecture Notes\", module7_lecture_notes),\n",
        "]\n",
        "\n",
        "module7_markdown = format_module(7, \"Logical Agents\", \n",
        "                         module7_sections, \n",
        "                         module7_definitions)\n",
        "display(Markdown(module7_markdown))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/markdown": "# Module 7: Logical Agents\n## AIMA Chapter 7.1 Knowledge-Based Agents\n\n\n## AIMA Chapter 7.2 The Wumpus World\n\n\n## AIMA Chapter 7.3 Logic\n\n\n## AIMA Chapter 7.4 Propositional Logic: A Very Simple Logic\n\n\n## AIMA 7.5 Propositional Theorem Proving\n\n\n## Module 7 Lecture Notes\n\n**Knowledge-based agents** use a process of reasoning over an internal representation of knowledge to decide what action to take. \n\nA KB contains a set of sentence that are written in a knowledge representation language. \n\nThe semantics defines the **truth** of each sentence with respect to a **possible world**, which we will often call a **model**. \n\nIf sentence α is true in model m: m satisfy α or m is a model of α \n\nOnly P True, Q False, P ⟹ Q is False. In other conditions, P ⟹ Q is True \n\nP ⇔ Q = P⟹Q ⋀ Q⟹P \n\n**Complex sentences** are constructed from simpler ones using **parentheses** and **logical connectives**. \n\nα ≡ β if and only if α⊨β and β⊨α \n\nConjunctive Normal Form (CNF): Every sentence of propositional logic is logically equivalent to a conjunction of clauses. Clauses are disjunctions of literals. \n\nResolution Algorithm: To show KB⊨α then we can show that KB ⋀ ¬α is unsatisfiable. \n\nclosed under resolution: If you apply resolution to a horn clause, you get back a horn clause \n\n¬ L1,1 ⋁ ¬ Breeze ⋁ B1,1 can be written as the implication L1,1 ⋀ Breeze ⟹ B1,1 \n\nForward Chaining is a kind of data-driven reasoning. \n\nBackward chaining works backwards from a query \n\nBackward chaining is a form of goal-directed reasoning \n\n\n\n## Module 7 Definitions\n* **Axioms** - – a sentence that is given \n* **Derived sentences** - a new sentence that is derived from others sentences\n* **Inference** - The process of deriving new sentences from old sentences\n* **Semantics of the sentences** - their meaning\n* **M(α)** - set of all models of α\n* **Entailment ⊨** - a sentence follows logically from another sentence α⊨β if and only if M(α) ⊆ M(β)\n* **Kb ⊢i α** - α is derived from KB by i\n* **Atomic sentences** - represented with a single propositional symbols\n* **Propositional symbols** - a statement that can be true or false\n* **¬(not)** - negation\n* **⋀(and)** - conjunction\n* **⋁(or)** - disjunction\n* **⟹ (implies)** - W⟹ S implication, W premise or antecede, S conclusion or consequence\n* **⇔ (if and only if)** - biconditional\n* **Soundness** - inference algorithm should only derive entailed sentences.\n* **Completeness** - if it can derive all sentences that are entailed\n* **Logically equivalent ≡** - they are true in the same set of models\n* **Commutativity** - (α ⋀ β) ≡ (β ⋀ α)\n* **Associativity** - ((α ⋀ β) ⋀ ɣ) ≡ (α ⋀ (β ⋀ ɣ))\n* **Contraposition** - (α ⟹ β) ≡ (¬β ⟹ ¬α)\n* **Implication elimination** - (α ⟹ β) ≡ (¬α ⋁ β)\n* **Biconditional elimination** - (α ⇔ β) ≡ ((α ⟹ β) ⋀ (β ⟹α))\n* **De morgan** - ¬(α ⋀ β) ≡ (¬α ⋁ ¬β)\n* **Distributivity of ⋀ over ⋁** - ((α ⋀ β) ⋁ ɣ) ≡ ((α ⋀ β) ⋁ (α ⋀ ɣ)))\n* **Distributivity of ⋁ over ⋀** - ((α ⋁ β) ⋀ ɣ) ≡ ((α ⋁ β) ⋀ (α ⋁ ɣ)))\n* **Monotonicity** - if KB⊨α then KB ⋀ β ⊨α\n* **Eliminate ⟹** - α ⟹ β with ¬α ⋁ β\n* **Unit resolution** - If ℓi and m are complementary literals, then we can eliminate them\n* **Definite clause** - disjunction of literals where exactly one is positive\n* **Horn clause** - disjunction of literals where at most one is positive\n",
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vX7lbnJd4sT5"
      },
      "source": [
        "# Your Exam Notes\n",
        "\n",
        "Here are your full set of exam notes that you can use on your midterm.  Choose **Runtime > Run all**, then your notes will be displayed.\n",
        "\n",
        "If you are taking the exam in person, then you must print a copy of your notes for yourself.   Here's how to print:\n",
        "* Run the cell below. \n",
        "* Click its \"Mirror cell in tab\" button (this is located in the upper right corner of the cell, immediately to the right of the trash can).  This will open the cell.  \n",
        "* In Chrome, you can then print your notes using the **File > Print** option from the browser's menu.  \n",
        "* In the print options, change the layout from Landscape to Portrait. \n",
        "* Clicking the Save, will save a PDF that you can then print.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 6207
        },
        "id": "T3cm1WV542_a",
        "outputId": "ecf90981-1994-4b52-acba-49adef404a7c"
      },
      "source": [
        "# This will generate the full set of notes that you can use for your exam.\n",
        "full_markdown = \"\\n\\n\".join([module1_markdown, \n",
        "                             module2_markdown, \n",
        "                             module3_markdown, \n",
        "                             module4_markdown, \n",
        "                             module5_markdown,\n",
        "                             module6_markdown,\n",
        "                             module7_markdown,]\n",
        "                       )\n",
        "display(Markdown(full_markdown))"
      ],
      "execution_count": null,
      "outputs": [
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          "data": {
            "text/markdown": "# Module 1: Rational Agents and Task Environments\n## AIMA Chapter 1.1 What is AI?\nformal definition of intelligence called rationality—loosely speaking, doing the “right thing\" \n\nsome consider intelligence to be a property of internal thought processes and reasoning, while others focus on intelligent behavior, an external characterization \n\ncapabilities for turing test: natural language processing, knowledge representation, automated reasoning, machine learning, computer vision, robotics \n\nlearn about human thought: introspection, psychological experiments, brain imaging \n\nAn agent is just something that acts \n\nAn agent is anything that perceives its environment through sensors and can act on its environment through actuators \n\nA percept is the agent’s perceptual inputs at any given instance. \n\nThe agent program runs on the physical architecture to produce f \n\nagent = architecture + program \n\na rational agent selects an action a to maximize its performance measure \n\nA rational agent is one that acts so as to achieve the best outcome or, when there is uncertainty, the best expected outcome. \n\nPEAS: to specify a task environment: Performance measure, Environment, Actuators, Sensors \n\nrational-agent vs laws of thought: more general--correct inference is just one of possible mechanisms. \n\nmore amenable to scientific development \n\nAI has focused on the study and construction of agents that do the right thing(defined by human). standard model \n\nConstruct agent FUNCTION f that maximizes the expected value of the performance measure, \n\nDesign an agent PROGRAM that implements f on a particular architecture \n\nsearch problem: goal, search problem: States, Actions, Performance measure. solution \n\n\n\n## AIMA Chapter 27.1 The Limits of AI\n\n\n## AIMA Chapter 27.1 Can Machines Really Think?\n\n\n## AIMA 2.1 Agents and Environments\n\n\n## AIMA 2.2 Good Behavior: The Concept of Rationality\n\n\n## AIMA 2.3 The Nature of Environments\n\n\n## AIMA 2.4 The Structure of Agents\n\n\n## Module 1 Lecture Notes\n\n\n## Module 1 Definitions\n* **Agent** - anything that can perceive and act in an environment\n* **Percept** - inputs from agents' sensors\n* **Other concept** - your definitions here\n* **Etc.** - your definitions here\n\n\n# Module 2: Python\n## Module 2 Lecture Notes\n Python: dynamic typing Drawback: type errors are only caught at runtime \n\nImmutable: string, tuple \n\nmutable: list \n\nkey of the dinctionary must be immutable \n\ncomprehension: newlist = [x for x in fruits if \"a\" in x] \n\nnewlist = [x if x != \"banana\" else \"orange\" for x in fruits] \n\n\n\n\n## Module 2 Definitions\n* **Mutability** - your definition here\n\n\n# Module 3: Search Problems\n## AIMA Chapter 3.1 Problem-Solving Agents\n\n\n## AIMA Chapter 3.2 Example Problems\n\n\n## AIMA Chapter 3.3 Search Algorithms\n\n\n## AIMA Chapter 3.4 Uninformed Search Strategies\n\n\n## Module 3 Lecture Notes\nFully observable=Deterministic=Known environment \n\nPartially observable or Nondeterministic \n\nDefinition: States, initial state, Actions, Transition Model, Path cost, Goal test \n\nTree Search: Enumerate in some order all possible paths from the initial state. Search through explicit tree generation \n\nNodes in search tree generated through transition model \n\nThe EXPAND function uses the Actions and Transition Model to create the corresponding states: creates new nodes, fills in the various fields \n\nTree search Problem: Failure to detect repeated states can turn a linear problem into an exponential one! \n\nsolution: Graph Search: must keep track of all possible states (can use a lot of memory) \n\nUninformed search: AKA “Blind search” Uses only information available in problem definition \n\nStrategy = order of tree expansion \n\nCompleteness- always find the solution? \n\nOptimality - finds a least cost solution (lowest path cost) first? \n\nBFS: frontier is FIFO (First-In-First-Out) Queue. Complete? Yes (if b is finite) Optimal? Yes\n\nTime Complexity: O(b^d) Space: O(b^d) \n\nDFS: frontier is LIFO (Last-In-First-Out) Queue \n\nComplete? No. It fails in infinite-depth spaces, spaces with loops \n\nIf we modify it to avoid repeated states along path, then it is complete in finite spaces. Optimal? No \n\ntime: O(b^m) Space: O(bm)  m:max depth \n\nDepth-limited search: Depth-First search but with depth limit l. If l < d then incomplete. If l > d then not optimal \n\nTime: O(b^l), space: O(bl) \n\nIterative deepening search: Complete & optimal. Time: O(b^d), Space: O(bd) \n\n\n\n## Module 3 Definitions\n* **Problem-solving agent** - an agent that can formulate a plan via search\n* **Reflex agents** - one that selects an action based only on the current percept and ignores the rest of the percept history\n* **Search** - the computational process that it undertakes.\n* **Solution** - The sequence that agent will consider actions that form a path to a goal state.\n* **State space** - the set of all states reachable from the initial state by any sequence of actions\n* **Path** - a sequence of actions leading from one state sj to another state sk\n* **Solution** - a path from the initial state si to a state sf that satisfies the goal test\n* **Search tree** - a way of representing the paths that a search algorithm has explored.\n* **Frontier** - those states that are available for expanding\n* **Optimal solution** - A solution is optimal if no solution has a lower path cost.\n\n\n# Module 4: Informed Search\n## AIMA Chapter 3.5 Informed (Heuristic) Search Strategies\n\n\n## AIMA Chapter 3.6 Heuristic Functions\n\n\n## Module 4 Lecture Notes\n\nAn informed search strategy uses domain-specific information about the location of the goals in order to find a solution more efficiently than uninformed search. \n\nuniform-cost search (UCS): step cost=1. \n\nDifference with BFS: Tests if a node is a goal state when it is selected for expansion, not when it is added to the frontier \n\nBest-first search: node selected for expansion based on an evaluation function f(n) (includes estimate of distance to goal) \n\nA heuristic function h(n) takes a state n and returns an estimate of the distance from n to the goal. \n\nGreedy best-first search: f(n) = h(n) Completely ignores g(n): the cost to get to n \n\nnot optimal, not complete can get stuck in loops \n\nA* search: Key Idea: avoid expanding paths that are already expensive, but expand most promising first. f(n)=g(n) + h(n) \n\nA heuristic h(n) is admissible/optimistic if it never overestimates the cost to reach the goal;  \n\nInadmissible (pessimistic) heuristics: break optimality by pushing good plans too far back on the frontier, which means they may never get expanded. \n\nIf h(n) is admissible, A* using Tree Search is optimal \n\nRelaxed problems: A problem with fewer restrictions on the actions than the original \n\nThe cost of an optimal solution to a relaxed problem is an admissible heuristic for the original problem \n\nDominance: If h2(n) ≥ h1(n) for all n (both admissible) then h2 dominates h1 \n\n\n\n## Module 4 Definitions\n* **Concept** - definition\n\n\n# Module 5: Adversarial Search and Games\n## AIMA Chapter 5.1 Game Theory\n\n\n## AIMA Chapter 5.2 Optimal Decisions in Games\n\n\n## AIMA Chapter 5.3 Heuristic Alpha–Beta Tree Search\n\n\n## AIMA Chapter 5.5 Stochastic Games\n\n\n## AIMA Chapter 16.1 Combining Beliefs and Desires under Uncertainty\n\n\n## AIMA Chapter 16.2 The Basis of Utility Theory\n\n\n## AIMA Chapter 16.3 Utility Functions\n\n\n## Module 5 Lecture Notes\n \nfully observable = perfect information \n\nStrategic: The next state is determined by the current state and the action executed by the agent and the actions of one other agent. \n\nZero-sum: one player’s loss is another’s gain \n\nGames as search: Initial state, Successor function, Terminal test, Utility function \n\nEvaluation functions: f(n) Evaluates how good a ‘board position’ is \n\nminimax value: the best achievable utility against a rational (optimal) adversary \n\nAlpha-Beta Pruning: α: MAX’s current lower bound on MAX’s outcome \n\nβ: MIN’s current upper bound on MIN’s outcome \n\nWhen evaluating a MAX node: a value v ≥ β is backed-up. MIN will never select that MAX node \n\nWhen evaluating a MIN node: a value v ≤ α is found. MAX will never select that MIN node \n\nExpectimax search: compute the average score under optimal play \n\nObjectivist / frequentist answer: Averages over repeated experiments \n\nSubjectivist / Bayesian answer: Degrees of belief about unobserved variables \n\n\n\n## Module 5 Definitions\n* **Concept** - definition\n\n\n# Module 6: Constraint Satisfaction Problems\n## AIMA Chapter 6.1 Defining Constraint Satisfaction Problems\n\n\n## AIMA Chapter 6.2 Constraint Propagation: Inference in CSPs\n\n\n## AIMA Chapter 6.3 Backtracking Search for CSPs\n\n\n## AIMA Chapter 6.4 Local Search for CSPs\n\n\n## AIMA Chapter 6.5 The Structure of Problems\n\n\n## Module 6 Lecture Notes\nIdentification: assignments to variables The goal itself is important, not the path \n\nCSPs are specialized for **identification problems** \n\nRepresent the constraints that solutions must satisfy in a uniform declarative language \n\nFind solutions by GENERAL PURPOSE search algorithms with no changes from problem to problem \n\nA **CSP** consists of: Finite set of variables, Nonempty domain of possible values for each variable, Finite set of constraints \n\nA **consistent** assignment does not violate the constraints \n\nAn assignment is **complete** when every variable is assigned a value. \n\nA solution to a CSP is a complete, consistent assignment \n\nConstraint graph: **nodes** are variables, **arcs** are (binary) constraints \n\nA binary CSP: each constraint relates two variables \n\nPreference (soft constraints) can be represented by a cost for each variable assignment  \n\nUnary constraints involve a single variable \n\nA CSP can easily be expressed as a search problem: \n\n**Initial State**: the empty assignment \n\n**Successor function**: Assign value to any unassigned variable provided that there is not a constraint conflict. \n\n**Goal test**: the current assignment is complete \n\n**Path cost**: a constant cost for every step \n\nvariables of domain size d, Branching factor at the root is n*d \n\nTree has n!*d^n leaves \n\nDepth-first search for CSPs with single-variable assignments is called **backtracking search** (uninformed algorithm for CSPs) \n\n**General-purpose** methods & **general-purpose** heuristics can give huge gains in speed, **on average** \n\nvariable should be assigned next: 1. Most **constrained** variable(with the fewest legal values) 2. (if ties:) Most **constraining** variable (with the most constraints on remaining variables) \n\nvariable’s values be tried: Least constraining value(the one that rules out the fewest values in the remaining variables) \n\ndetect inevitable failure early: **Forward checking** (Keep track of remaining legal values for unassigned variables) \n\nTerminate search when any unassigned variable has no remaining legal values\n\n**Constraint propagation** goes beyond forward checking & repeatedly enforces constraints locally \n\nCSP solvers combine search(assigning a value to a variable) and inference(Constraint propagation) \n\nX -> Y is consistent iff for every value x of X there is some allowed y \n\nSearch: Use constraints to add labels to find one solution \n\nConstraint Propagation: Use constraints to eliminate labels to simultaneously find all solutions \n\nAC-3 improvements: \n1. At each iteration, we only need to examine those Xi where at least one neighbor of Xi has lost a value in the previous iteration \n\n2. If Xi loses a value only because of arc inconsistencies with Yj , we don’t need to check Yj on the next iteration. \n\n3. Removing a value on Xi can only make Yj arc inconsistent with respect to Xi itself. Thus, we only need to check that (j,i) is still arc-consistent.\n\n\n## Module 6 Definitions\n* **Node consistency** - satisfies unary constraints\n* **Arc consistency** - satisfies binary constraints\n* **Ac-3 time complexity** - (n^2d^3)\n\n\n# Module 7: Logical Agents\n## AIMA Chapter 7.1 Knowledge-Based Agents\n\n\n## AIMA Chapter 7.2 The Wumpus World\n\n\n## AIMA Chapter 7.3 Logic\n\n\n## AIMA Chapter 7.4 Propositional Logic: A Very Simple Logic\n\n\n## AIMA 7.5 Propositional Theorem Proving\n\n\n## Module 7 Lecture Notes\n\n**Knowledge-based agents** use a process of reasoning over an internal representation of knowledge to decide what action to take. \n\nA KB contains a set of sentence that are written in a knowledge representation language. \n\nThe semantics defines the **truth** of each sentence with respect to a **possible world**, which we will often call a **model**. \n\nIf sentence α is true in model m: m satisfy α or m is a model of α \n\nOnly P True, Q False, P ⟹ Q is False. In other conditions, P ⟹ Q is True \n\nP ⇔ Q = P⟹Q ⋀ Q⟹P \n\n**Complex sentences** are constructed from simpler ones using **parentheses** and **logical connectives**. \n\nα ≡ β if and only if α⊨β and β⊨α \n\nConjunctive Normal Form (CNF): Every sentence of propositional logic is logically equivalent to a conjunction of clauses. Clauses are disjunctions of literals. \n\nResolution Algorithm: To show KB⊨α then we can show that KB ⋀ ¬α is unsatisfiable. \n\nclosed under resolution: If you apply resolution to a horn clause, you get back a horn clause \n\n¬ L1,1 ⋁ ¬ Breeze ⋁ B1,1 can be written as the implication L1,1 ⋀ Breeze ⟹ B1,1 \n\nForward Chaining is a kind of data-driven reasoning. \n\nBackward chaining works backwards from a query \n\nBackward chaining is a form of goal-directed reasoning \n\n\n\n## Module 7 Definitions\n* **Axioms** - – a sentence that is given \n* **Derived sentences** - a new sentence that is derived from others sentences\n* **Inference** - The process of deriving new sentences from old sentences\n* **Semantics of the sentences** - their meaning\n* **M(α)** - set of all models of α\n* **Entailment ⊨** - a sentence follows logically from another sentence α⊨β if and only if M(α) ⊆ M(β)\n* **Kb ⊢i α** - α is derived from KB by i\n* **Atomic sentences** - represented with a single propositional symbols\n* **Propositional symbols** - a statement that can be true or false\n* **¬(not)** - negation\n* **⋀(and)** - conjunction\n* **⋁(or)** - disjunction\n* **⟹ (implies)** - W⟹ S implication, W premise or antecede, S conclusion or consequence\n* **⇔ (if and only if)** - biconditional\n* **Soundness** - inference algorithm should only derive entailed sentences.\n* **Completeness** - if it can derive all sentences that are entailed\n* **Logically equivalent ≡** - they are true in the same set of models\n* **Commutativity** - (α ⋀ β) ≡ (β ⋀ α)\n* **Associativity** - ((α ⋀ β) ⋀ ɣ) ≡ (α ⋀ (β ⋀ ɣ))\n* **Contraposition** - (α ⟹ β) ≡ (¬β ⟹ ¬α)\n* **Implication elimination** - (α ⟹ β) ≡ (¬α ⋁ β)\n* **Biconditional elimination** - (α ⇔ β) ≡ ((α ⟹ β) ⋀ (β ⟹α))\n* **De morgan** - ¬(α ⋀ β) ≡ (¬α ⋁ ¬β)\n* **Distributivity of ⋀ over ⋁** - ((α ⋀ β) ⋁ ɣ) ≡ ((α ⋀ β) ⋁ (α ⋀ ɣ)))\n* **Distributivity of ⋁ over ⋀** - ((α ⋁ β) ⋀ ɣ) ≡ ((α ⋁ β) ⋀ (α ⋁ ɣ)))\n* **Monotonicity** - if KB⊨α then KB ⋀ β ⊨α\n* **Eliminate ⟹** - α ⟹ β with ¬α ⋁ β\n* **Unit resolution** - If ℓi and m are complementary literals, then we can eliminate them\n* **Definite clause** - disjunction of literals where exactly one is positive\n* **Horn clause** - disjunction of literals where at most one is positive\n",
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