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COMPLETENESS VIA CORRESPONDENCE FOR EXTENSIONS OF THE LOGIC OF PARADOX

  • BARTELD KOOI (a1) and ALLARD TAMMINGA (a2)
Abstract
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.

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*FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN, OUDE BOTERINGESTRAAT 52, 9712 GL GRONINGEN, THE NETHERLANDS E-mail: b.p.kooi@rug.nl, a.m.tamminga@rug.nl
INSTITUTE OF PHILOSOPHY, UNIVERSITY OF OLDENBURG, AMMERLÄNDER HEERSTRASSE 114–118, 26129 OLDENBURG, GERMANY E-mail: allard.tamminga@uni-oldenburg.de
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G. Priest (1979). The logic of paradox. Journal of Philosophical Logic, 8, 219241.

H. Sahlqvist (1975). Completeness and correspondence in the first and second order semantics for modal logic. In S. Kanger , editor. Proceedings of the Third Scandinavian Logic Symposium. Amsterdam: North-Holland Publishing Company, pp. 110143.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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