On fuzzification of propositional logics

✍ Scribed by Branislav Boričić

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 108 KB
• Volume: 108
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00369-2

✦ Synopsis

By fuzziÿcation we mean a procedure which assigns a fuzzy logic to an arbitrary crisp logic. In this paper we describe two essentially di erent fuzziÿcation procedures. In order to give a formal description of the notion of fuzziness of a formula, we extend the language of the propositional logic by a family of unary propositional operators, inductively applicable to the formulae. The set of all formulae provable in an arbitrary propositional crisp logic is extended by the fuzziness measure axioms concerning those operators. A logical system obtained in such a way, making possible to express a fuzziness measure of truthfulness of any formula in context of the observed logic, can be considered as a kind of polymodal logic. This example includes a description of the Kripke-type possible worlds semantics covering the considered logical systems, being followed by the corresponding completeness results. The second example presents quite a syntactic concept of fuzziÿcation, including some of the usual proof-theoretical results such as the cut-elimination theorem.