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Generalized Kripke Frames

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Abstract

Algebraic work [9] shows that the deep theory of possible world semantics is available in the more general setting of substructural logics, at least in an algebraic guise. The question is whether it is also available in a relational form.This article seeks to set the stage for answering this question. Guided by the algebraic theory, but purely relationally we introduce a new type of frames. These structures generalize Kripke structures but are two-sorted, containing both worlds and co-worlds. These latter points may be viewed as modelling irreducible increases in information where worlds model irreducible decreases in information. Based on these structures, a purely model theoretic and uniform account of completeness for the implication-fusion fragment of various substructural logics is given. Completeness is obtained via a generalization of the standard canonical model construction in combination with correspondence results.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico, 88003, USA

    Mai Gehrke

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  1. Mai Gehrke
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Correspondence to Mai Gehrke.

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The author’s research was partially supported by grant NSF01-4-21760 of the USA National Science Foundation as well as by a grant from the Carlsberg Foundation.

Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen

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Gehrke, M. Generalized Kripke Frames. Stud Logica 84, 241–275 (2006). https://doi.org/10.1007/s11225-006-9008-7

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  • DOI: https://doi.org/10.1007/s11225-006-9008-7

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