A Normal Form which Preserves Tautologies and Contradictions in a Class of Fuzzy Logics

Benjamin Bedregal

Most normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve either tautologies or contradictions which are fundamental for automatic theorem provers based on refutation methods. De Morgan implicative systems are triples like the De Morgan system, but considering fuzzy implications instead of t-conorms. These systems can be used to evaluate the formulas of a propositional language based on the logical connectives of negation, conjunction and implication. Therefore, it determines different fuzzy logics, called De Morgan implicative.In this paper, we will introduce a normal form for that language and we will show that, for the case of the De Morgan implicative fuzzy logics whose t-norms are strict, this normal form preserves contradictions as well as tautologies.

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