A Characterization of Classic-Like Fuzzy Semantics

A normal form which preserves tautologies and contradictions in a class of fuzzy logics

“…they have as 1-tautologies exactly the classical tautologies [3,4]. So, since INF(α) ≡ α for the propositional classic logic, the INF for the classic-like fuzzy semantics restricted to the conjunction, negation and implication connectives, clearly preserves tautologies and contradictions.…”

A Fuzzy Semantic for BDI Logic

“…In this section we show a generic informal semantics found in the BDI logics [5,7] and based on this informal semantics, in Section 2 we define a semantic approach of a fuzzy BDI Logic using the classic-like fuzzy semantics defined in [20] and the first family of manyvalued modal logic described by Fitting in [21]. In Section 3 are shown related work the BDI agents and applications.…”

“…Others fuzzy (or many-valued) modal logics have already been defined (see for example [21][22][23][24][25][26][27]). In the approach proposed in [23,28], the propositional connectives are interpreted as t-norms, t-conorms, fuzzy implications, fuzzy negations are considered in such a way that the classical tautologies are preserved as in [20,29] and the modal connectives have a semantic similar to the proposed by Caicedo and Rodríguez [30]. In particular, the authors seek a characterisation of fuzzy connective which maintains the usual theorems of modal logic into fuzzy setting.…”

“…Fitting [21], in particular, investigates two families of many-valued modal logics and the first one determines the truth value of a modal formula based on its sub-formulae values in each accessible world. This notion is extended in this paper to a fuzzy BDI semantics where the notions of t-norms, t-conorms, fuzzy negations, implication and bi-implication [18,20,[31][32][33] to give semantic, respectively, to the propositional connectives and, ∨, ¬, →, and ↔. (1) T is a triangular norm (t-norm) if it satisfies commutativity, associativity, monotonicity and 1 acts like an identity element (1-identity).…”

On the Boolean-like Law I(x, I(y, x)) = 1

“…This paper reports a further investigation exposed in. 6 Here, we will produce necessary and sufficient conditions under which the Booleanlike law (1) …”