相关论文: Isabelle: The Next 700 Theorem Provers

To address the increasing size and complexity of modern software systems, compositional verification separates the verification of single components from the verification of their composition. In architecture-based verification, the former…

With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…

We present techniques for reasoning about constructor classes that (like the monad class) fix polymorphic operations and assert polymorphic axioms. We do not require a logic with first-class type constructors, first-class polymorphism, or…

Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…

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…

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error…

This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…

In this paper we present an efficient approach to implementing model checking in the Higher Order Logic (HOL) of Isabelle. This is a non-trivial task since model checking is restricted to finite state sets. By restricting our scope to…

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…

A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on…

We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several datasets consisting of questions asking for the truth or falsity…

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…

Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…

Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is…

This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this…

While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…

Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…

Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…