Related papers: Teaching a Formalized Logical Calculus

We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…

In this paper we present a tableau proof system for first order logic of proofs FOLP. We show that the tableau system is sound and complete with respect to Mkrtychev models of FOLP.

Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared…

This paper presents a special subset of the first-order predicate logic named S-program calculus (briefly S-calculus). The S-calculus is a calculus consisting of so-called S-formulas that are defined over the abstract state space of a…

We present a new modular proof method of termination for second-order computation, and report its implementation SOL. The proof method is useful for proving termination of higher-order foundational calculi. To establish the method, we use a…

Our research is part of a wider project that aims to investigate and reason about the correctness of scheme-based source code transformations of Erlang programs. In order to formally reason about the definition of a programming language and…

Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…

In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…

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…

Transitive closure logic is a known extension of first-order logic obtained by introducing a transitive closure operator. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive…

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the…

This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…

Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…

We study the first-order primal infon logic. It is the core of the policy language DKAL. We provide Gentzen-style calculi for two versions of this logic that are not equivalent. For both versions we investigate the semantics: one of them is…

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…

We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…

These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

This paper studies a first-order expansion of a combination C+J of intuitionistic and classical propositional logic, which was studied by Humberstone (1979) and del Cerro and Herzig (1996), from a proof-theoretic viewpoint. While C+J has…

This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…