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Title

On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice

AuthorsBou, Felix; Esteva, Francesc ; Godo, Lluis ; Rodriguez, Ricardo O.
KeywordsFuzzy logic
Many-valued modal logic
Modal logic
Substructural logic
Many-valued logic
Issue Date2011
PublisherOxford University Press
CitationJournal of Logic and Computation 21: 739- 790 (2011)
AbstractThis article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements and the ones only evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truth-constants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truth-constants in the language. © 2009 The Author.
URIhttp://hdl.handle.net/10261/138239
DOI10.1093/logcom/exp062
Identifiersdoi: 10.1093/logcom/exp062
issn: 0955-792X
Appears in Collections:(IIIA) Artículos
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