Related papers: On Incorrectness Logic and Kleene Algebra with Top…
Fine-tuning Large Language Models (LLMs) with reinforcement learning to produce an explicit Chain-of-Thought (CoT) before answering produces models that consistently raise overall performance on code, math, and general-knowledge benchmarks.…
Hoare logic is a foundation of axiomatic semantics of classical programs and it provides effective proof techniques for reasoning about correctness of classical programs. To offer similar techniques for quantum program verification and to…
Chain-of-Thought (CoT) prompting has been widely recognized for its ability to enhance reasoning capabilities in large language models (LLMs). However, our study reveals a surprising contradiction to this prevailing perspective within the…
Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning.…
Language models trained via outcome-based reinforcement learning (RL) to reason using chain-of-thought (CoT) have shown remarkable performance. Monitoring such a model's CoT may allow us to understand its intentions and detect potential…
Verifying the correctness of a textual statement requires not only semantic reasoning about the meaning of words, but also symbolic reasoning about logical operations like count, superlative, aggregation, etc. In this work, we propose…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
Large Reasoning Models (LRMs) achieve promising performance but compromise token efficiency due to verbose reasoning processes. Unconscious Thought Theory (UTT) posits that complex problems can be solved more efficiently through…
Final-answer-based metrics are commonly used for evaluating large language models (LLMs) on math word problems, often taken as proxies for reasoning ability. However, such metrics conflate two distinct sub-skills: abstract formulation…
Existing Computerized Adaptive Testing (CAT) frameworks typically select questions based on the predicted likelihood that the student will answer correctly. This design ignores information contained in students' open-ended responses,…
Recent advances in large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, particularly on contest-based mathematical benchmarks like the IMO. However, these contests do not reflect the depth,…
Chain-of-Thought (CoT) prompting has significantly advanced task-solving capabilities in natural language processing with large language models. Unlike standard prompting, CoT encourages the model to generate intermediate reasoning steps,…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
Chain-of-Thought (CoT) reasoning has demonstrated remarkable effectiveness in enhancing the reasoning abilities of large language models (LLMs). However, its efficiency remains a challenge due to the generation of excessive intermediate…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…
Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key…
The concept of a Kleene algebra (sometimes also called Kleene lattice) was already generalized by the first author for non-distributive lattices under the name pseudo-Kleene algebra. We extend these concepts to posets and show how…