Open AccessCorrespondence Analysis for First Degree Entailment
Author(s) -
Я. И. Петрухин
Publication year - 2016
Publication title -
logičeskie issledovaniâ
Language(s) - English
Resource type - Journals
eISSN - 2413-2713
pISSN - 2074-1472
DOI - 10.21146/2074-1472-2016-22-1-108-124
Subject(s) - unary operation , logical consequence , propositional calculus , negation , extension (predicate logic) , rule of inference , natural deduction , inference , mathematics , truth table , degree (music) , natural number , star (game theory) , algorithm , discrete mathematics , computer science , artificial intelligence , programming language , physics , acoustics , mathematical analysis
In this paper natural deduction systems for four-valued logic $FDE$ (first degree entailment) and its extensions are constructed. At that B. Kooi and A. Tamminga’s method of correspondence analysis is used. All possible four-valued unary $\star$ and binary $\circ $ propositional connectives which could be added to $FDE$ are considered. Then $FDE$ is extended by Boolean negation $\sim$and every entry (line) of truth tables for $\star$ and $\circ $is characterized by inference scheme. By adding all inference schemes characterizing truth tables for $\star$ and $\circ $as rules of inference to the natural deduction for $FDE$, natural deduction for extension of $FDE$ is obtained. In addition, applying of correspondence analysis gives axiomatizations of implicative extensions of $FDE$ including $BN4$ and some extensions by classical implications.