Work

A Sequent Calculus for Satisfiability and Validity

Year: 2024

Type: article

Abstract: This paper presents a new sequent calculus that integrates rules for testing both satisfiability and validity within the same logical system. Its notion of deduction encompasses both nonlogical and logical assumptions. A formula is considered consistent when it has a certain deduction from nonlogical assumptions, and it is considered provable if there is a certain deduction for it from logical assumptions. The equivalences between provability and validity, as well as between consistency and satisfiability, are proved. All the structural rules are admissible, and extensions with nonlogical rules are shown to overcome Post-completeness.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.14245481

Author: Beraldo de Araujo, Anderson

Institutions: Universidade Estadual de Campinas (UNICAMP), University of Minho

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Air Force Office of Scientific Research

Award: G7952474138