Polynomial ring calculus for modal logics: A new semantics and proof method for modalities: Polynomial ring calculus for modal logics

Review of Symbolic Logic 4 (1):150-170 (2011)
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Abstract

A new proof style adequate for modal logics is defined from the polynomial ring calculus. 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 S 5, and can be easily extended to other modal logics.

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10.1017/s1755020310000213

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Citations of this work

Polynomial semantics for modal logics.Juan C. Agudelo-Agudelo & Santiago Echeverri-Valencia - 2019 - Journal of Applied Non-Classical Logics 29 (4):430-449.

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References found in this work

Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
Two Dogmas of Empiricism.W. V. Quine - 1951 - Philosophical Review 60 (1):20-43.
Modal Logic.Marcus Kracht - 2002 - Bulletin of Symbolic Logic 8 (2):299-301.

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