Conditional dichotomy, the contrast between two outputs conditioned on the same context, is vital for applications such as debate, defeasible inference, and causal reasoning. Existing methods that rely on semantic similarity often fail to capture the nuanced oppositional dynamics essential for these applications. Motivated by these limitations, we introduce a novel task, Conditional Dichotomy Quantification (ConDQ), which formalizes the direct measurement of conditional dichotomy and provides carefully constructed datasets covering debate, defeasible natural language inference, and causal reasoning scenarios. To address this task, we develop the Dichotomy-oriented Geometric Embedding (DoGE) framework, which leverages complex-valued embeddings and a dichotomous objective to model and quantify these oppositional relationships effectively. Extensive experiments validate the effectiveness and versatility of DoGE, demonstrating its potential in understanding and quantifying conditional dichotomy across diverse NLP applications. Our code and datasets are available at https://github.com/cui-shaobo/conditional-dichotomy-quantification.

Crafting an appealing heading is crucial for attracting readers and marketing work or products. A popular way is to summarize the main idea with a refined description and a memorable acronym. However, there lacks a systematic study and a formal benchmark including datasets and metrics. Motivated by this absence, we introduce LOgogram, a novel benchmark comprising 6,653 paper abstracts with corresponding descriptions and acronyms. To measure the quality of heading generation, we propose a set of evaluation metrics from three aspects: summarization, neology, and algorithm. Additionally, we explore three strategies for heading generation(generation ordering, tokenization of acronyms, and framework design) under various prevalent learning paradigms(supervised fine-tuning, in-context learning with Large Language Models(LLMs), and reinforcement learning) on our benchmark. Our experimental results indicate the difficulty in identifying a practice that excels across all summarization, neologistic, and algorithmic aspects.

Defeasibility in causal reasoning implies that the causal relationship between cause and effect can be strengthened or weakened. Namely, the causal strength between cause and effect should increase or decrease with the incorporation of strengthening arguments (supporters) or weakening arguments (defeaters), respectively. However, existing works ignore defeasibility in causal reasoning and fail to evaluate existing causal strength metrics in defeasible settings. In this work, we present 𝛿-CAUSAL, the first benchmark dataset for studying defeasibility in causal reasoning. 𝛿-CAUSAL includes around 11K events spanning ten domains, featuring defeasible causality pairs, namely, cause-effect pairs accompanied by supporters and defeaters. We further show that current causal strength metrics fail to reflect the change of causal strength with the incorporation of supporters or defeaters in 𝛿-CAUSAL. To this end, we propose CESAR (Causal Embedding aSsociation with Attention Rating), a metric that measures causal strength based on token-level causal relationships. CESAR achieves a significant 69.7% relative improvement over existing metrics, increasing from 47.2% to 80.1% in capturing the causal strength change brought by supporters and defeaters. We further demonstrate even Large Language Models (LLMs) like GPT-3.5 still lag 4.5 and 10.7 points behind humans in generating supporters and defeaters, emphasizing the challenge posed by 𝛿-CAUSAL.