POLYNOMIAL RING CALCULUS FOR MODAL LOGICS: A NEW SEMANTICS AND PROOF METHOD FOR MODALITIES-Reference-Cited by-同舟云学术

POLYNOMIAL RING CALCULUS FOR MODAL LOGICS: A NEW SEMANTICS AND PROOF METHOD FOR MODALITIES

Published:2010-09-14 Issue:1 Volume:4 Page:150-170
ISSN:1755-0203
Container-title:The Review of Symbolic Logic
language:en
Short-container-title:Rev. symb. logic

Author:

AGUDELO JUAN C.,CARNIELLI WALTER

Abstract

A new (sound and complete) proof style adequate for modal logics is defined from the polynomial ring calculus (PRC). The new semantics not only expresses truth conditions of modal formulas by means of polynomials, but also permits to perform deductions through polynomial handling. This paper also investigates relationships among the PRC here defined, the algebraic semantics for modal logics, equational logics, the Dijkstra–Scholten equational-proof style, and rewriting systems. The method proposed is throughly exemplified for S5, and can be easily extended to other modal logics.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy,Mathematics (miscellaneous)

Reference23 articles.

1. Algebraic semantics for modal logics II

2. Equational logic;Taylor;Houston Journal of Mathematics,1979

3. Predicate Calculus and Program Semantics

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