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Multi-hop reasoning requires aggregating multiple documents to answer a complex question. Existing methods usually decompose the multi-hop question into simpler single-hop questions to solve the problem for illustrating the explainable…
Designing algorithms with provable guarantees that also work well in practice remains difficult, requiring both mathematical reasoning and careful implementation. Existing approaches that bridge worst-case theory and empirical performance,…
We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…
With the continuous advancement of Large Language Models (LLMs), intelligent agents are becoming increasingly vital. However, these agents often fail in environments governed by implicit rules--hidden constraints that cannot be observed…
This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language…
Enabling more concise and modular proofs is essential for advancing formal reasoning using interactive theorem provers (ITPs). Since many ITPs, such as Rocq and Lean, use tactic-style proofs, learning higher-level custom tactics is crucial…
Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated.…
PyLog is a minimal experimental proof assistant based on linearised natural deduction for intuitionistic and classical first-order logic extended with a comprehension operator. PyLog is interesting as a tool to be used in conjunction with…
Software startups develop innovative, software-intensive product and services. This context leads to uncertainty regarding the software they are building. Experimentation, a process of testing hypotheses about the product, helps these…
This book chapter establishes connections between the interactive proof tool Isabelle and classical tableau and resolution technology. Isabelle's classical reasoner is described and demonstrated by an extended case study: the Church-Rosser…
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
Induction lies at the heart of mathematics and computer science. However, automated theorem proving of inductive problems is still limited in its power. In this abstract, we first summarize our progress in automating inductive theorem…
We study the problem active sequential hypothesis testing, also known as pure exploration: given a new task, the learner adaptively collects data from the environment to efficiently determine an underlying correct hypothesis. A classical…
Programmers often use an iterative process of hypothesis generation ("perhaps this function is called twice?") and hypothesis testing ("let's count how many times this breakpoint fires") to understand the behavior of unfamiliar or…
{log} ('setlog') is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FSTRA). As such, it can be used as an automated theorem prover (ATP) for this theory. {log} is able to automatically…
Proof engineering efforts using interactive theorem proving have yielded several impressive projects in software systems and mathematics. A key obstacle to such efforts is the requirement that the domain expert is also an expert in the…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
During the past decade of continuous development, the theorem prover Vampire has become an automated solver for the combined theories of commonly-used data structures. Vampire now supports arithmetic, induction, and higher-order logic.…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
The process of scientific discovery relies on an interplay of observations, analysis, and hypothesis generation. Machine learning is increasingly being adopted to address individual aspects of this process. However, it remains an open…