The Review of Symbolic Logic

Research Articles

COMPLETENESS VIA CORRESPONDENCE FOR EXTENSIONS OF THE LOGIC OF PARADOX

BARTELD KOOIa1 c1 and ALLARD TAMMINGAa2 c2

a1 Faculty of Philosophy, University of Groningen

a2 Faculty of Philosophy, University of Groningen, Institute of Philosophy, University of Oldenburg

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.

(Received April 17 2012)

Correspondence:

c1 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

c2 INSTITUTE OF PHILOSOPHY, UNIVERSITY OF OLDENBURG, AMMERLÄNDER HEERSTRASSE 114–118, 26129 OLDENBURG, GERMANY E-mail: allard.tamminga@uni-oldenburg.de