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|Title:||On The Set Of Intermediate Logics Between The Truth- And Degree-preserving Aukasiewicz Logics|
Marcelo E.; Esteva
|Abstract:||The aim of this article is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic L and its degree-preserving companion L=. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L= 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.|
Paraconsistent And Explosive Logics
|Editor:||Oxford Univ Press|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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