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Proceedings of the 2021 Workshop on Semantic Spaces at the Intersection of NLP, Physics, and Cognitive Science (SemSpace)
Martha Lewis

Mehrnoosh Sadrzadeh
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Understanding the Semantic Space: How Word Meanings Dynamically Adapt in the Context of a Sentence
Nora AguirreCelis

Risto Miikkulainen
How do people understand the meaning of the word “small” when used to describe a mosquito, a church, or a planet? While humans have a remarkable ability to form meanings by combining existing concepts, modeling this process is challenging. This paper addresses that challenge through CEREBRA (ContextdEpendent meaning REpresentations in the BRAin) neural network model. CEREBRA characterizes how word meanings dynamically adapt in the context of a sentence by decomposing sentence fMRI into words and words into embodied brainbased semantic features. It demonstrates that words in different contexts have different representations and the word meaning changes in a way that is meaningful to human subjects. CEREBRA’s contextbased representations can potentially be used to make NLP applications more humanlike.
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LinPP: a Pythonfriendly algorithm for Linear Pregroup Parsing
Irene Rizzo
We define a linear pregroup parser, by applying some key modifications to the minimal parser defined in (Preller, 2007). These include handling words as separate blocks, and thus respecting their syntactic role in the sentence. We prove correctness of our algorithm with respect to parsing sentences in a subclass of pregroup grammars. The algorithm was specifically designed for a seamless implementation in Python. This facilitates its integration within the DisCopy module for QNLP and vastly increases the applicability of pregroup grammars to parsing realworld text data.
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A CCGBased Version of the DisCoCat Framework
Richie Yeung

Dimitri Kartsaklis
While the DisCoCat model (Coecke et al., 2010) has been proved a valuable tool for studying compositional aspects of language at the level of semantics, its strong dependency on pregroup grammars poses important restrictions: first, it prevents largescale experimentation due to the absence of a pregroup parser; and second, it limits the expressibility of the model to contextfree grammars. In this paper we solve these problems by reformulating DisCoCat as a passage from Combinatory Categorial Grammar (CCG) to a category of semantics. We start by showing that standard categorial grammars can be expressed as a biclosed category, where all rules emerge as currying/uncurrying the identity; we then proceed to model permutationinducing rules by exploiting the symmetry of the compact closed category encoding the word meaning. We provide a proof of concept for our method, converting “Alice in Wonderland” into DisCoCat form, a corpus that we make available to the community.
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Grammar equations
Bob Coecke

Vincent Wang
Diagrammatically speaking, grammatical calculi such as pregroups provide wires between words in order to elucidate their interactions, and this enables one to verify grammatical correctness of phrases and sentences. In this paper we also provide wirings within words. This will enable us to identify grammatical constructs that we expect to be either equal or closely related. Hence, our work paves the way for a new theory of grammar, that provides novel ‘grammatical truths’. We give a nogotheorem for the fact that our wirings for words make no sense for preordered monoids, the form which grammatical calculi usually take. Instead, they require diagrams – or equivalently, (free) monoidal categories.
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On the Quantumlike Contextuality of Ambiguous Phrases
Daphne Wang

Mehrnoosh Sadrzadeh

Samson Abramsky

Victor Cervantes
Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a welldefined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics’ contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaftheoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of ContextualitybyDefault (CbD), we explore the probabilistic variants of these and show that CbDcontextuality is also possible.
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Conversational Negation using Worldly Context in Compositional Distributional Semantics
Benjamin Rodatz

Razin Shaikh

Lia Yeh
We propose a framework to model an operational conversational negation by applying worldly context (prior knowledge) to logical negation in compositional distributional semantics. Given a word, our framework can create its negation that is similar to how humans perceive negation. The framework corrects logical negation to weight meanings closer in the entailment hierarchy more than meanings further apart. The proposed framework is flexible to accommodate different choices of logical negations, compositions, and worldly context generation. In particular, we propose and motivate a new logical negation using matrix inverse. We validate the sensibility of our conversational negation framework by performing experiments, leveraging density matrices to encode graded entailment information. We conclude that the combination of subtraction negation and phaser in the basis of the negated word yields the highest Pearson correlation of 0.635 with human ratings.
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Parsing conjunctions in DisCoCirc
Tiffany Duneau
In distributional compositional models of meaning logical words require special interpretations, that specify the way in which other words in the sentence interact with each other. So far within the DisCoCat framework, conjunctions have been implemented as merging both conjuncts into a single output, however in the new framework of DisCoCirc merging between nouns is no longer possible. We provide an account of conjunction and an interpretation for the word ‘and’ that solves this, and moreover ensures certain intuitively similar sentences can be given the same interpretations.
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Should Semantic Vector Composition be Explicit? Can it be Linear?
Dominic Widdows

Kristen Howell

Trevor Cohen
Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations for ‘wet’ and ‘fish’, how should the concept ‘wet fish’ be represented? This position paper surveys this question from two points of view. The first considers the question of whether an explicit mathematical representation can be successful using only tools from within linear algebra, or whether other mathematical tools are needed. The second considers whether semantic vector composition should be explicitly described mathematically, or whether it can be a modelinternal sideeffect of training a neural network. A third and newer question is whether a compositional model can be implemented on a quantum computer. Given the fundamentally linear nature of quantum mechanics, we propose that these questions are related, and that this survey may help to highlight candidate operations for future quantum implementation.