Canonicity and Completeness Results for Many Valued Modal Logics
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Nomikos, C.
Koutras, C. D.
Peppas, P.
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peer reviewed
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Journal of Applied Non Classical Logics
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We prove frame determination results for the family of many-valued modal logics introduced by M. Fitting in the early '90s. Each modal language of this family is based on a Heyting algebra, which serves as the space of truth values, and is interpreted on an interesting version of possible-worlds semantics: the modal frames are directed graphs whose edges are labelled with an element of the under- lying Heyting algebra. We introduce interesting generalized forms of the classical axioms D, T, B, 4, and 5 and prove that they are canonical for certain algebraic frame properties, which generalize seriality, re°exivity, symmetry, transitivity and euclideanness. Our results are quite general as they hold for any modal language built on a complete Heyting algebra
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en
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Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικής