46 research outputs found
leanCoP: lean connection-based theorem proving
AbstractThe Prolog programimplements a theorem prover for classical first-order (clausal) logic which is based on the connection calculus. It is sound and complete (provided that an arbitrarily large I is iteratively given), and demonstrates a comparatively strong performance
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
A Tableaux Calculus for Reducing Proof Size
A tableau calculus is proposed, based on a compressed representation of
clauses, where literals sharing a similar shape may be merged. The inferences
applied on these literals are fused when possible, which reduces the size of
the proof. It is shown that the obtained proof procedure is sound,
refutationally complete and allows to reduce the size of the tableau by an
exponential factor. The approach is compatible with all usual refinements of
tableaux.Comment: Technical Repor
Lemmas: Generation, Selection, Application
Noting that lemmas are a key feature of mathematics, we engage in an
investigation of the role of lemmas in automated theorem proving. The paper
describes experiments with a combined system involving learning technology that
generates useful lemmas for automated theorem provers, demonstrating
improvement for several representative systems and solving a hard problem not
solved by any system for twenty years. By focusing on condensed detachment
problems we simplify the setting considerably, allowing us to get at the
essence of lemmas and their role in proof search
Investigations into Proof Structures
We introduce and elaborate a novel formalism for the manipulation and
analysis of proofs as objects in a global manner. In this first approach the
formalism is restricted to first-order problems characterized by condensed
detachment. It is applied in an exemplary manner to a coherent and
comprehensive formal reconstruction and analysis of historical proofs of a
widely-studied problem due to {\L}ukasiewicz. The underlying approach opens the
door towards new systematic ways of generating lemmas in the course of proof
search to the effects of reducing the search effort and finding shorter proofs.
Among the numerous reported experiments along this line, a proof of
{\L}ukasiewicz's problem was automatically discovered that is much shorter than
any proof found before by man or machine.Comment: This article is a continuation of arXiv:2104.1364
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions
PROVA AUTOMATIZADA DE TEOREMA EM LĂ“GICA PROPOSICIONAL
Este trabalho aborda o desenvolvimento de um sistema para prova automatizada de teoremas em lógica proposicional. O artigo apresenta os fundamentos teóricos gerais, questões operacionais e a estrutura de um software de prova de teoremas, elaborado com propósitos acadêmicos e didáticos, utilizando métodos de prova baseados em três tipos de tableaux semânticos: tableau de Smullyan, tableau com Lema e tableau KE. Experimentos foram realizados para verificar a correção dos resultados das provas, utilizando fórmulas geradas automaticamente.AbstractThis work describes the development of an automated theorem proving system of propositional logic. The paper presents the theoretical foundations, operational issues and structure of a theorem proving software, developed with academic and didactic purposes, using proof methods based on three semantics tableaux: Smullyan tableau, Lema tableau e KE tableau. Experiments were performed to verify the correctness of the results of the proofs, using automatically generating formulas
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book