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Canonical Extensions and Kripke–Galois Semantics for Non-distributive Logics

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Abstract

This article presents an approach to the semantics of non-distributive propositional logics that is based on a lattice representation (and duality) theorem that delivers a canonical extension of the lattice. Our approach supports both a plain Kripke-style semantics and, by restriction, a general frame semantics. Unlike the framework of generalized Kripke frames (RS-frames), the semantic approach presented in this article is suitable for modeling applied logics (such as temporal, or dynamic), as it respects the intended interpretation of the logical operators. This is made possible by restricting admissible interpretations.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Applied Sciences of Thessaly (TEI of Thessaly), Larissa, Greece

    Chrysafis Hartonas

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  1. Chrysafis Hartonas
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Correspondence to Chrysafis Hartonas.

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Presented at Unilog’18, Vichy, France, as the winner of the Aristotle Logic Prize and co-runner for the Universal Logic Prize 2018.

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Hartonas, C. Canonical Extensions and Kripke–Galois Semantics for Non-distributive Logics. Log. Univers. 12, 397–422 (2018). https://doi.org/10.1007/s11787-018-0195-6

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  • DOI: https://doi.org/10.1007/s11787-018-0195-6

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