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

  • JUAN C. AGUDELO (a1) and WALTER CARNIELLI (a2)

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.

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Corresponding author

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

  • JUAN C. AGUDELO (a1) and WALTER CARNIELLI (a2)

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