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On the set of intermediate logics between the truth- and degree-preserving Łukasiewicz logics

AuthorsConiglio, Marcelo E.; Esteva, Francesc ; Godo, Lluis
KeywordsIntermediate logic
Degree-preserving logic
Logical matrices
Paraconsistent and explosive logics
Truth-preserving logic
Łukasiewicz logic
Issue Date2016
PublisherOxford University Press
CitationLogic Journal of the IGPL 24: 288- 320 (2016)
AbstractThe aim of this article is to explore the class of intermediate logics between the truth-preserving Łukasiewicz logic Ł and its degree-preserving companion Ł≤. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in Ł≤ and derivable in L and we characterize the corresponding intermediate logics. From a semantical point of view, we first consider the family of logics characterized by matrices defined by lattice filters in [0,1], but we show there are intermediate logics falling outside this family. Finally, we study the case of finite-valued Lukasiewicz logics where we axiomatize a large family of intermediate logics defined by families of matrices (A,F) such that A is a finite MV-algebra and F is a lattice filter.
Identifiersdoi: 10.1093/jigpal/jzw006
issn: 1368-9894
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