This paper deals with propositional fuzzy modal logic with evaluated syntax based on MV-algebras. We focus on its semantical theory from the viewpoint of Pavelka’s graded semantics of propositional fuzzy logic, investigate the L-tautologies based on different Kripke frames. We also define the notion of Lsemantical consequence operation, its some basic properties are obtained. Finally, this pape...

In this paper we present several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. Based on different characterizations of necessity measures on fuzzy sets, a group of logics with Kripke style semantics are built over a restricted language, namely a two level language composed of non-modal and modal formulas, the latter ...

In this paper we study modal extensions of Product fuzzy logic with both relational semantics based on Kripke structures with crisp accessibility relations and algebraic semantics, when the underlying product fuzzy logic is expanded with truth-constants, the ∆ operator and with two infinitary inference rules. We provide completeness results for both kinds of semantics. Finally, we also consider...

In this paper we present completeness results of several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. In a first attempt, based on different characterizations of necessity measures on fuzzy sets, a group of logics, with Kripke style semantics, are built over a restricted language, indeed a two level language compose...

There are two kinds of bisimulation, namely crisp and fuzzy, between fuzzy structures such as automata, labeled transition systems, Kripke models interpretations in description logics. Fuzzy bisimulations automata over a complete residuated lattice have been introduced by ?iri? et al. 2012. Logical characterizations (respectively, logics) the [0,1] with Gödel t-norm provided Fan 2015 Nguyen 202...

We consider the Gödel bi-modal logic determined by fuzzy Kripke models where both the propositions and the accessibility relation are infinitely valued over the standard Gödel algebra [0,1] and prove strong completeness of Fischer Servi intuitionistic modal logic IK plus the prelinearity axiom with respect to this semantics. We axiomatize also the bi-modal analogues of T, S4, and S5 obtained by...

Supervaluationism and fuzzy logic are two complementary formalisms for reasoning with vague information. We study a framework for combining both approaches. Supervaluationism is modeled by a space of precisifications, essentially a Kripke structure. We equip this space with a probability measure to extract the truth value of each propositional variable by measuring the set of precisifications i...

Formal verification methods model systems by Kripke structures. In order to model live behaviors of systems, Kripke structures are augmented with fairness conditions. Such conditions partition the computations of the systems into fair computations, with respect to which verification proceeds, and unfair computations, which are ignored. Reasoning about Kripke structures augmented with fairness i...

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the manyvalued semantics of Gödel logic. The calculi are used to establish completeness and complexity results for these fragments.