Same Formulas, Different Semantics: Do Language Models Follow Modal Logic Specifications?

Both expressions of uncertainty and inferences are ubiquitous in natural language, and valid inferences over natural-language expressions of uncertainty are necessary for not only everyday conversations but also for high-stakes domains such as medicine and law. While large language models are increasingly evaluated on logical reasoning tasks, disentangling principled, symbolic reasoning from clever surface-level pattern matching is fraught with difficulty. We introduce a benchmark for reasoning over probability operators--inference over sentences with gradable epistemic modals (e.g., probably, might, must) containing 14,320 procedurally-generated English prompts across fifteen inference templates, systematically varying question form, negation strategy, and surface content. Evaluating 29 models, we find that most show answer biases independent of the logical form, a systematic preference for Yes or No. We summarize this with a competence floor: the worse of a model's accuracy on Yes-correct and No-correct items. Only 9 of 29 models exceed random chance. We also test variations in question form, verb phrases/activity, and both the gender and origin of names used in the prompts, finding biases across every axis.

Language models (LMs) struggle with logical tasks like reasoning on syllogisms. It has been shown that Knowledge Representation (KR) plays a crucial role in expressing input information to help models solve tasks. This observation motivates our study of the impact of different formal KR notations on syllogistic reasoning by extending the FOLIO and P-FOLIO datasets. Our experiments on Small Language Models (SLMs) in Supervised Fine-Tuning (SFT) and Zero-Shot (ZS) settings show that the choice of input notation can yield performances competitive with natural language while enabling faster inference. We also propose a syllogistic categorization method (SEF) and use it to enrich ZS prompts with logical definitions, which boost reasoning in small models. We open-source our framework, Common Logic Grammar Construction (CLGC), as the first Python library for automatically generating syllogisms in KR notations and defining their SEF categories.

Humans effortlessly go beyond literal meanings: If you mow the lawn, I will give you fifty dollars, is typically understood as implying that the speaker will pay only if the lawn is mowed, whereas If you are hungry, there is pizza in the oven implies that pizza is available regardless of the hearers hunger. Large Language Models - LLMs - show human-like performance on many tasks, yet it remains unclear whether they reason like humans. To address this, we conducted a population-matching experiment assessing how twentyfive LLMs compute conditional inferences across four languages, compared to an equal number of humans per language. We find that humans enrich logical reasoning through pragmatic inferences across languages. Model behavior is more variable. Some LLMs perfectly follow the truth-table of conditionals but they ignore pragmatic inferences, while others deviate from the truth-table, adhering to a single interpretation across the board, thus reflecting accurate rule-based processing but not human-like reasoning. Overall, LLMs are accurate semantic operators, but fail to capture the pragmatic enrichments characteristic of human reasoning. Crucially, LLM accuracy is neither predicted nor boosted by open vs. closed status, training orientation, or architecture type, suggesting that pragmatic reasoning is still an emerging ability in the cognitive toolkit of artificial systems.