相关论文: Lash 1.0 (System Description)

Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…

MaLeS is an automatic tuning framework for automated theorem provers. It provides solutions for both the strategy finding as well as the strategy scheduling problem. This paper describes the tool and the methods used in it, and evaluates…

TLA+ is a specification language based on standard set theory and temporal logic that has constructs for hierarchical proofs. We describe how to write TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's mutual…

Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…

Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…

Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s.…

TLAPS, the TLA+ proof system, is a platform for the development and mechanical verification of TLA+ proofs written in a declarative style requiring little background beyond elementary mathematics. The language supports hierarchical and…

Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…

Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…

Propositional Linear Temporal Logic (LTL) is a popular formalism for specifying desirable requirements and security and privacy policies for software, networks, and systems. Yet expressing such requirements and policies in LTL remains…

Several successful strategies in automated reasoning rely on human-supplied guidance about which term or clause shapes are interesting. In this paper we aim to discover interesting term shapes automatically. Specifically, we discover…

We present a novel means of describing local image appearances using binary strings. Binary descriptors have drawn increasing interest in recent years due to their speed and low memory footprint. A known shortcoming of these representations…

Explainable artificial intelligence (XAI) is one of the most intensively developed area of AI in recent years. It is also one of the most fragmented with multiple methods that focus on different aspects of explanations. This makes difficult…

Reasoning is a fundamentally algorithmic task. Yet current work on LLM-based reasoning relies on free-form generation whose theoretical guarantees (soundness, completeness, complexity, optimality) remain poorly understood. We argue that we…

Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s.…

LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…

The use of a functional language to implement proof strategies as proof tactics in interactive theorem provers, often provides short, concise and elegant implementations. Whilst being elegant, the use of higher order features and combinator…

Recently, the description logic LE-ALC was introduced for reasoning in the semantic environment of the enriched formal contexts, and a tableaux algorithm was developed for checking the consistency of ABoxes in this logic. In this paper, we…

We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). Unlike most learning based approaches, we focus on generalising from very little training data and…