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

Published online by Cambridge University Press:  14 September 2010

JUAN C. AGUDELO  and
WALTER CARNIELLI
JUAN C. AGUDELO*
Affiliation:
State University of Campinas—UNICAMP, and Eafit University
WALTER CARNIELLI*
Affiliation:
State University of Campinas—UNICAMP, and SQIG—IT
*
*PH.D. PROGRAM IN PHILOSOPHY, AREA OF LOGIC, IFCH AND GROUP FOR APPLIED AND THEORETICAL LOGIC—CLE, STATE UNIVERSITY OF CAMPINAS—UNICAMP, BRAZIL AND LOGIC AND COMPUTATION RESEARCH GROUP, EAFIT UNIVERSITY, COLOMBIA. E-mail: juancarlos@cle.unicamp.br
†DEPARTMENT OF PHILOSOPHY AND GROUP FOR APPLIED AND THEORETICAL LOGIC, CENTRE FOR LOGIC, EPISTEMOLOGY AND THE HISTORY OF SCIENCE—CLE, STATE UNIVERSITY OF CAMPINAS—UNICAMP, BRAZIL AND SQIG—INSTITUTE OF TECHNOLOGY, LISBON, PORTUGAL. E-mail:walter.carnielli@cle.unicamp.br
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 1 , March 2011 , pp. 150 - 170
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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