NDLI: On Gentzen Relations Associated with Finite-valued Logics Preserving Degrees of Truth

Content Provider	Springer Nature Link
Author	Gil, Angel J.
Copyright Year	2013
Abstract	When considering m-sequents, it is always possible to obtain an m-sequent calculus VL for every m-valued logic (defined from an arbitrary finite algebra L of cardinality m) following for instance the works of the Vienna Group for Multiple-valued Logics. The Gentzen relations associated with the calculi VL are always finitely equivalential but might not be algebraizable. In this paper we associate an algebraizable 2-Gentzen relation with every sequent calculus VL in a uniform way, provided the original algebra L has a reduct that is a distributive lattice or a pseudocomplemented distributive lattice. We also show that the sentential logic naturally associated with the provable sequents of this algebraizable Gentzen relation is the logic that preserves degrees of truth with respect to the original algebra (in contrast with the more common logic that merely preserves truth). Finally, for some particular logics we obtain 2-sequent calculi that axiomatize the algebraizable Gentzen relations obtained so far.
Starting Page	749
Ending Page	781
Page Count	33
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	101
Issue Number	4
e-ISSN	15728730
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-06-28
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Algebraic logic Gentzen system Gentzen relation Logics preserving degrees of truth Distributive lattices Pseudocomplemented distributive lattices Logic Mathematical Logic and Foundations Computational Linguistics
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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