Related papers: A modest proposal: explicit support for foundation…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the forall-quantifier or lambda-binder are just…
Tree of Thoughts (ToT) is a reasoning strategy for Large Language Models (LLMs) that employs a generator to suggest reasoning steps and a discriminator to decide which steps to implement. ToT demonstrates strong performance on reasoning…
Large language models (LMs) beyond a certain scale, demonstrate the emergent capability of generating free-text rationales for their predictions via chain-of-thought (CoT) prompting. While CoT can yield dramatically improved performance,…
We observe today a large diversity of proof systems. This diversity has the negative consequence that a lot of theorems are proved many times. Unlike programming languages, it is difficult for these systems to co-operate because they do not…
An Achilles heel of Large Language Models (LLMs) is their tendency to hallucinate non-factual statements. A response mixed of factual and non-factual statements poses a challenge for humans to verify and accurately base their decisions on.…
Self-Consistency samples diverse reasoning chains with answers and chooses the final answer by majority voting. It is based on forward reasoning and cannot further improve performance by sampling more reasoning chains when saturated. To…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
Reasoning in large language models is often discussed as a single capability, but some of its gains may stem from simpler underlying operations. We examine two such primitives, recall and state-tracking, through five controlled task…
This paper proposes a novel prompting approach, Judgment of Thought (JoT), specifically tailored for binary logical reasoning tasks. Despite advances in prompt engineering, existing approaches still face limitations in handling complex…
Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token…
Neural Theorem Proving (NTP) employs LLMs to automate formal proofs in proof assistants. While LLMs have achieved relatively remarkable success in informal reasoning tasks using natural languages, the transition to mechanized formal theorem…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
Neither the classical nor intuitionistic logic traditions are perfectly-aligned with the purpose of reasoning about computation, in that neither tradition can permit unconstrained recursive definitions without inconsistency: recursive…
Recent Long-Context Language Models (LCLMs) can process hundreds of thousands of tokens in a single prompt, enabling new opportunities for knowledge-intensive multi-hop reasoning by integrating large sets of retrieved documents or, in some…
Latent reasoning via continuous chain-of-thoughts (Latent CoT) has emerged as a promising alternative to discrete CoT reasoning. Operating in continuous space increases expressivity and has been hypothesized to enable superposition: the…
We develop a proof-theoretic semantics (P-tS) for second-order logic (S-oL), providing an inferentialist alternative to both full and Henkin model-theoretic interpretations. Our approach is grounded in base-extension semantics (B-eS), a…
Temporal reasoning is the task of predicting temporal relations of event pairs. While temporal reasoning models can perform reasonably well on in-domain benchmarks, we have little idea of these systems' generalizability due to existing…
Chain-of-thought (CoT) is a method that enables language models to handle complex reasoning tasks by decomposing them into simpler steps. Despite its success, the underlying mechanics of CoT are not yet fully understood. In an attempt to…
In language reasoning, longer chains of thought consistently yield better performance, which naturally suggests that visual latent reasoning may likewise benefit from longer latent sequences. However, we discover a counterintuitive…