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Completeness via correspondence for extensions of the logic of paradox

Kooi, B. & Tamminga, A., Dec-2012, In : The Review of Symbolic Logic. 5, 4, p. 720 - 730 11 p.

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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.

Original languageEnglish
Pages (from-to)720 - 730
Number of pages11
JournalThe Review of Symbolic Logic
Volume5
Issue number4
Publication statusPublished - Dec-2012

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