Fuzzy logic, continuity and effectiveness

Abstract. It is shown the complete equivalence between the theory of continuous (enumeration) fuzzy closure operators and the theory of (effective) fuzzy deduction systems in Hilbert style. Moreover, it is proven that any truth-functional semantics whose connectives are interpreted in [0,1] by continuous functions is axiomatizable by a fuzzy deduction system (but not by an effective fuzzy deduction system, in general).

• Type: Journal
• Year: 2002
• Where: AML
• Authors: Loredana Biacino, Giangiacomo Gerla
• Keywords: AML 2002, Effective Fuzzy Deduction, Fuzzy Closure Operators, Fuzzy Deduction