NDLI: A Non-deterministic View on Non-classical Negations

Content Provider	Springer Nature Link
Author	Avron, Arn
Copyright Year	2005
Abstract	We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ$^{+}$, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which is based on non-deterministic four-valued or three-valued structures, and prove soundness and completeness for all of them. We show that the role of each rule is to reduce the degree of non-determinism in the corresponding systems. We also show that all the systems considered are decidable, and our semantics can be used for the corresponding decision procedures. Most of the extensions of LJ$^{+}$ (with or without ff) are shown to be conservative over the underlying logic, and it is determined which of them are not.
Starting Page	159
Ending Page	194
Page Count	36
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	80
Issue Number	2-3
e-ISSN	15728730
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Non-deterministic Semantics Negation Many-valued Logics Constructive Logics Paraconsistent Logics Logic Mathematical Logic and Foundations Computational Linguistics
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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