Correspondence Analysis for First Degree Entailment

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Я. И. Петрухин

Аннотация

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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Как цитировать
[1]
Я. И. Петрухин. Correspondence Analysis for First Degree Entailment // Логические исследования / Logical Investigations. 2018. Т. 22. № 1.
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Раздел
Неклассические логики