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On the relation between modal and multi-modal logics over Lukasiewicz logic

AutorEsteva, Francesc ; Godo, Lluis ; Rodriguez, Ricardo
Palabras claveLukasiewicz
Fuzzy systems
Modal logic
Many valued logics
Fecha de publicación9-jul-2017
EditorInstitute of Electrical and Electronics Engineers
CitaciónIEEE International Conference on Fuzzy Systems, FUZZ 2017: Article number 80157032017 (2017)
ResumenIn a previous paper, it was shown that the (minimal) modal logic Mc¿n with fuzzy accessibility relations over the finite-valued ¿ukasiewicz logic ¿n and a corresponding multimodal logic mM¿cn (with a modality a for each value a in the n-valued ¿n-chain) had the same expressive power when the language is extended with truth-constants. In this paper we partially extend these results when replacing the underlying logic ¿n by the infinite-valued ¿ukasiewicz logic (with rational truth constants in the language). We prove that the (standard) tautologies of the modal logic M¿c (resp. mM¿c) are in fact the common tautologies of all the logics M¿cn (resp. all the logics mM¿cn) when letting n vary over N. This fact opens the door to show an alternative proof of the finite model property for these logics and hence their decidability. © 2017 IEEE.
URIhttp://hdl.handle.net/10261/164483
Identificadoresdoi: 10.1109/FUZZ-IEEE.2017.8015703
issn: 10987584
isbn: 978-150906034-4
Aparece en las colecciones: (IIIA) Comunicaciones congresos
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