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Non-deterministic Semantics for Intuitionistic Paraconsistent Logics
| Content Provider | CiteSeerX |
|---|---|
| Author | Avron, Arnon |
| Abstract | this paper we show that one can conservatively add to intuitionistic positive logic both types of negation. By this we get conservative extensions of intuitionistic logic which are LFIs (logics of Formal Inconsistency) in the sense of [5], as well as paraconsistent conservative extensions of intuitionistic positive logic which enjoy the relevance properties of the logic Pac from [2] (One of these logics is da Costa famous system C! ([6, 5])). The intuitionistic negation is added exactly as it is usually done in intuitionistic logic: by adding a bottom element ? (satisfying ? ` A for every A) and de ning the strong negation of A to be A ?. This results, of course, with the full propositional intuitionistic logic. This logic and its positive fragment serve then as bases for several conservative extensions having a nonexplosive negation respecting LEM. The weakest of these system is obtained by adding only LEM to positive intuitionistic logic. The strongest - by adding to full intuitionistic logic almost all the properties (with only one exception) of the negation of the maximal paraconsistent logics Pac and J 3 ([1, 2, 7, 8, 5]). We provide Gentzen-type systems for all these systems and prove an appropriate version of the non-analytic cut elimination theorem for them. We also provide Kripke-style semantics for all the logics, and prove soundness and completeness for this semantics. The main idea in our semantics is to allow a certain amount of nondeterminism in the valuations we use. We note that in the case of C! this semantics is signi cantly simpler than the one given in [4] |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Da Costa Famous System Positive Intuitionistic Logic Positive Fragment Serve Intuitionistic Logic Main Idea Kripke-style Semantics Certain Amount Relevance Property Logic Pac Full Propositional Intuitionistic Logic Intuitionistic Positive Logic Bottom Element Intuitionistic Negation Appropriate Version Formal Inconsistency Gentzen-type System Several Conservative Extension Non-analytic Cut Elimination Theorem Strong Negation Nonexplosive Negation Intuitionistic Paraconsistent Logic Non-deterministic Semantics Maximal Paraconsistent Logic Pac Paraconsistent Conservative Extension Full Intuitionistic Logic Conservative Extension |
| Content Type | Text |
| Resource Type | Article |
