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T-norm-based logics with an independent involutive negation. (English) Zbl 1114.03015
Summary: We investigate the addition of arbitrary independent involutive negations to t-norm-based logics. We deal with several extensions of MTL and establish general completeness results. Indeed, we show that, given any t-norm-based logic satisfying some basic properties, its extension by means of an involutive negation preserves algebraic and (finite) strong standard completeness. We deal with both propositional and predicate logics.

MSC:
03B50 Many-valued logic
03B52 Fuzzy logic; logic of vagueness
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