相关论文: Natural Deduction as Higher-Order Resolution

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, they did not have a systematic way to encode their expertise. To address this…

The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…

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 a formal theory of smooth vector fields, Lie groups and the Lie algebra of a Lie group in the theorem prover Isabelle. Lie groups are abstract structures that are composable, invertible and differentiable. They are…

We describe Imandra, a modern computational logic theorem prover designed to bridge the gap between decision procedures such as SMT, semi-automatic inductive provers of the Boyer-Moore family like ACL2, and interactive proof assistants for…

Table-based reasoning has shown remarkable progress in combining deep models with discrete reasoning, which requires reasoning over both free-form natural language (NL) questions and structured tabular data. However, previous table-based…

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…

We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…

A flexible infrastructure for normative reasoning is outlined. A small-scale demonstrator version of the envisioned system has been implemented in the proof assistant Isabelle/HOL by utilising the first authors universal logical reasoning…

We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…

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…

Recent work has shown that integrating large language models (LLMs) with theorem provers (TPs) in neuro-symbolic pipelines helps with entailment verification and proof-guided refinement of explanations for natural language inference (NLI).…

Learning first-order logic programs (LPs) from relational facts which yields intuitive insights into the data is a challenging topic in neuro-symbolic research. We introduce a novel differentiable inductive logic programming (ILP) model,…

We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…

An Isabelle/HOL formalisation of G\"odel's two incompleteness theorems is presented. The work follows \'Swierczkowski's detailed proof of the theorems using hereditarily finite (HF) set theory. Avoiding the usual arithmetical encodings of…

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…

Tackling Natural Language Inference with a logic-based method is becoming less and less common. While this might have been counterintuitive several decades ago, nowadays it seems pretty obvious. The main reasons for such a conception are…

The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…

In interactive theorem proving, formalization quality is a key factor for maintainability and re-usability of developments and can also impact proof-checking performance. Commonly, anti-patterns that cause quality issues are known to…

We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics…