Open AccessCorrespondence analysis for strong three-valued logic
Author(s) -
Allard Tamminga
Publication year - 2014
Publication title -
logičeskie issledovaniâ
Language(s) - English
Resource type - Journals
eISSN - 2413-2713
pISSN - 2074-1472
DOI - 10.21146/2074-1472-2014-20-0-253-266
Subject(s) - natural deduction , rule of inference , truth table , unary operation , mathematics , inference , logical connective , łukasiewicz logic , algebra over a field , operator (biology) , natural (archaeology) , computer science , algorithm , discrete mathematics , arithmetic , theoretical computer science , many valued logic , artificial intelligence , pure mathematics , substructural logic , description logic , history , biochemistry , chemistry , archaeology , repressor , transcription factor , gene
I apply Kooi and Tamminga’s (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these charac- terizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics. Among other things, I thus obtain a new proof system for _ukasiewicz’s three-valued logic.