Correspondence Analysis for First Degree Entailment


Y. I. Petrukhin


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.






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