On polynomial semantics for propositional logics. Issue 2 (2nd April 2016)

• Record Type: Journal Article
• Authors: Agudelo-Agudelo, Juan C.; Agudelo-González, Carlos A.; García-Quintero, Oscar E.
• Is Part Of: Journal of applied non-classical logics. Volume 26:Issue 2(2016)
• Page Start: 103
• Page End: 125
• Publication Date: 2016-04-02
• Subjects: Polynomial semantics -- finite-valued logic -- paraconsistent logic -- polynomials over finite fields -- Nullstellensatz for finite fields -- Gröbner basis; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2016.1198529
• Languages: English
• ISSNs: 1166-3081

Abstract

Abstract : Some properties and an algorithm for solving systems of multivariate polynomial equations over finite fields are presented. It is then shown how formulas of propositional logics (particularly of finite-valued logics and paraconsistent logics) can be translated into polynomials over finite fields in such a way that several logic problems are expressed in terms of algebraic problems. Consequently, algebraic properties and algorithms can be used to solve the algebraically-represented logic problems. The methods described herein combine and generalise those of various previous works.