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COMPLETENESS VIA CORRESPONDENCE FOR EXTENSIONS OF THE LOGIC OF PARADOX

Published online by Cambridge University Press:  30 July 2012

BARTELD KOOI  and
ALLARD TAMMINGA
BARTELD KOOI*
Affiliation:
Faculty of Philosophy, University of Groningen
ALLARD TAMMINGA*
Affiliation:
Faculty of Philosophy, University of Groningen, Institute of Philosophy, University of Oldenburg
*
*FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN, OUDE BOTERINGESTRAAT 52, 9712 GL GRONINGEN, THE NETHERLANDS E-mail: [email protected], [email protected]
†INSTITUTE OF PHILOSOPHY, UNIVERSITY OF OLDENBURG, AMMERLÄNDER HEERSTRASSE 114–118, 26129 OLDENBURG, GERMANY E-mail: [email protected]
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Abstract

Taking our inspiration from modal correspondence theory, we present the idea of correspondence analysis for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox (LP). First, we characterize each of the possible truth table entries for unary and binary operators that could be added to LP by an inference scheme. Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for LP. Third, we show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics.

Type
Research Articles
Information
The Review of Symbolic Logic , Volume 5 , Issue 4 , December 2012 , pp. 720 - 730
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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