arXiv subjects

Ricardo Oscar Rodriguez

Publications and source records attributed to Ricardo Oscar Rodriguez.

5 recordsLinked to original sources

arXiv2026

A Gödel Modal Logic Over Witnessed Models

We introduce GW, a Gödel modal logic based on Kripke models in which the value of each modal formula is witnessed by an accessible world. This witnessed semantics eliminates the limit-based phenomena that preclude the finite model property in the usual Kripke semantics for Gödel modal logics, thereby yielding a more constructive semantic framework. We present a sound and complete refutation calculus for GW and design a terminating backward proof-search procedure with countermodel generation. As a direct consequence of this procedure, GW enjoys the finite model property.

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arXiv2020

Axiomatization of crisp Godel modal logic

In this paper we consider the modal logic with both Box and Diamond arising fromKripke models with a crisp accessibility and whose propositions are valued over the stan-dard Godel algebra [0,1]G. We provide an axiomatic system extending the one from [3]for models with a valued accessibility with Dunn axiom from positive modal logics, andshow it is strongly complete with respect to the intended semantics. The axiomatizationsof the most usual frame restrictions are given too. We also prove that in the studied logicit is not possible to get Box as an abbreviation of Diamond, nor vice-versa, showing that indeedthe axiomatic system we present does not coincide with any ofthe mono-modal fragmentspreviously axiomatized in the literature.

math.LO↗

arXiv2016

Possibilistic semantics for a modal KD45 extension of Gödel fuzzy logic

In this paper we provide a simplified semantics for the logic KD45(G), i.e. the many-valued Gödel counterpart of the classical modal logic KD45. More precisely, we characterize KD45(G) as the set of valid formulae of the class of possibilistic Gödel Kripke Frames $\langle W,π\rangle$, where $W$ is a non-empty set of worlds and $π: W \longrightarrow [0, 1]$ is a normalized possibility distribution on $W$.

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arXiv2011

Bi-modal Gödel logic over [0,1]-valued Kripke frames

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 restricting to models over frames satisfying the [0,1]-valued versions of the structural properties which characterize these logics. As application of the completeness theorems we obtain a representation theorem for bi-modal Gödel algebras.

math.LO↗

arXiv2009

A Godel Modal Logic

In this paper we consider an approach where both propositions and the accessibility relation are infinitely many-valued over Gödel algebras. In particular, we consider separately the $\Box $-fragment and the $\Diamond $-fragment of our Gödel modal logic and prove that both logics are complete with respect to the class of models with values in the linear Hetying algebra [0,1]. In addition, we show that the first fragment is uniquely determined by the class of models having crisp accessibility relation but it has not the finite model property. On the contrary, the second fragment is not characterized by crisp accessibility models alone but it has the finite model property. Finally, we show that the approach can be extended to include finitely many rational truth-values à la Pavelka.

math.LO↗