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This article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements… (More)

This paper introduces a new class of fuzzy closure operators called implicative closure operators, which generalize some notions of fuzzy closure operators already introduced by different authors. We show that implicative closure operators capture some usual consequence relations used in Approximate Reasoning, like ChakrabortyÕs graded consequence relation,… (More)

One of the goals of a variety of approximate reasoning models is to cope with inference patterns more flexible than those of classical reasoning. Among them, similarity based reasoning aims at modeling notions of resemblance or proximity among propositions and consequence relations which make sense in such a setting. One way of proceeding is to. equip the… (More)

We prove strong completeness of the-version and the 3-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both in…nitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the …rst logic is reducible to the class of frames having two-valued… (More)

One of the ways to model contraction functions for belief sets is epistemic entrenchment. The first step was provided by Gärdenfors in [5], who defined epistemic entrenchment and a contraction function in terms of it and related the latter with the AGM contraction function. Later Hans Rott in [16] presented an entrenchment based contraction function that… (More)

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 pre-linearity axiom with respect to this semantics. We axiomatize also the bi-modal… (More)

We consider two kinds of similarity-based reasoning and formalise them in a logical setting. In one case, we are led by the principle that conclusions can be drawn even if they are only approximately correct. This leads to a graded approximate entailment, which is weaker than classical entailment. In the other case, we follow the principle that conclusions… (More)