Related papers: Extensional Higher-Order Paramodulation in Leo-III
We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…
Recent advances in large language models (LLMs) have popularized test-time scaling, where models generate additional reasoning tokens before producing final answers. These approaches have demonstrated significant performance improvements on…
Recent advancements in Large Language Models (LLMs) have shifted from explicit Chain-of-Thought (CoT) reasoning to more efficient latent reasoning, where intermediate thoughts are represented as vectors rather than text. However, latent…
Large Language Models (LLMs) have demonstrated remarkable reasoning abilities, prompting interest in their application as black-box optimizers. This paper asserts that LLMs possess the capability for zero-shot optimization across diverse…
Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
Large language models (LLMs) demonstrate impressive performance but lack the flexibility to adapt to human preferences quickly without retraining. In this work, we introduce Test-time Preference Optimization (TPO), a framework that aligns…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
Post-training has become the dominant recipe for turning a language model into a competent search-augmented reasoning agent. A line of recent work pushes its performance further by adding elaborate machinery on top of this standard…
In this project, a rather complete proof-theoretical formalization of Lambek Calculus (non-associative with arbitrary extensions) has been ported from Coq proof assistent to HOL4 theorem prover, with some improvements and new theorems.…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
Large Language Models (LLMs) have demonstrated strong reasoning capabilities in solving complex problems. However, current approaches primarily enhance reasoning through the elaboration of thoughts while neglecting the diversity of…
Large language models (LLMs) have recently shown strong progress on scientific reasoning, yet two major bottlenecks remain. First, explicit retrieval fragments reasoning, imposing a hidden "tool tax" of extra tokens and steps. Second,…
We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…
Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
We present Isabellm, an LLM-powered theorem prover for Isabelle/HOL that performs fully automatic proof synthesis. Isabellm works with any local LLM on Ollama and APIs such as Gemini CLI, and it is designed to run on consumer grade…
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…