arXiv subjects

Amanda Vidal

Publications and source records attributed to Amanda Vidal.

6 recordsLinked to original sources

arXiv2026

Axiomatizing logics of finite G\"odel-Kripke models

We investigate completeness for modal G\"odel logics with respect to finite G\"odel-Kripke models, along with related aspects. It is well known that the logics studied in [4, 11] fail to be complete with respect to finite G\"odel-Kripke models. We show that the natural candidate axiomatic extensions do not restore completeness, thereby resolving a 15 year open problem posed in the aforementioned works. We then provide new axiomatizations that are complete for finite models and characterize intermediate witnessing conditions that hold for the basic logics.

math.LO↗

arXiv2023

On the local consequence of modal Product logic: standard completeness and decidability

We study local consequence relations in modal extensions of product logic over Kripke models with either valued (fuzzy) or crisp accessibility relations. In both settings, we consider semantics over the full class of product algebras as well as over the standard product algebra on $[0,1]$. Our main result is a constructive reduction of these modal logics to propositional product logic. As consequences, we prove that all the resulting systems are decidable and standard complete, i.e., the local consequence relation over all product algebras coincides with the one induced by the standard product algebra. In the valued-accessibility case, our methods strengthen previous results on decidability by extending them from theoremhood to arbitrary local consequence relations, and covering standard completeness. In the crisp case, the techniques are substantially different and yield, to the best of our knowledge, the first decidability and standard completeness results for local modal product logics with crisp accessibility relations.

math.LO↗

arXiv2021

Undecidability and non-axiomatizability of modal many-valued logics

In this work we study the decidability of a class of global modal logics arising from Kripke frames evaluated over certain residuated lattices, known in the literature as modal many-valued logics. We exhibit a large family of these modal logics which are undecidable, in contrast with classical modal logic and propositional logics defined over the same classes of algebras. This family includes the global modal logics arising from Kripke frames evaluated over the standard Lukasiewicz and Product algebras. We later refine the previous result, and prove that global modal Lukasiewicz and Product logics are not even recursively axiomatizable. We conclude by solving negatively the open question of whether each global modal logic coincides with its local modal logic closed under the unrestricted necessitation rule.

math.LO↗

arXiv2019

Axiomatizing logics of fuzzy preferences using graded modalities

The aim of this paper is to propose a many-valued modal framework to formalize reasoning with both graded preferences and propositions, in the style of van Benthem et al.'s classical modal logics for preferences. To do so, we start from Bou et al.'s minimal modal logic over a finite and linearly ordered residuated lattice. We then define appropriate extensions on a multi-modal language with graded modalities, both for weak and strict preferences, and with truth-constants. Actually, the presence of truth-constants in the language allows us to show that the modal operators Box and Diamond of the minimal modal logic are inter-definable. Finally, we propose an axiomatic system for this logic in an extended language (where the preference modal operators are definable), and prove completeness with respect to the intended graded preference semantics.

cs.LO↗

arXiv2019

On Transitive modal many-valued logics

This paper is focused on the study of modal logics defined from valued Kripke frames, and particularly, on computability and expressibility questions of modal logics of transitive Kripke frames evaluated over certain residuated lattices. It is shown that a large family of those logics -- including the ones arising from the standard MV and Product algebras -- yields an undecidable consequence relation. Later on, the behaviour of transitive modal Lukasiewicz logic is compared with that of its non transitive counterpart, exhibiting some particulars concerning computability and equivalence with other logics. We conclude the article by showing the undecidability of the validity and the local SAT questions over transitive models when the Delta operation is added to the logic.

cs.LO↗

arXiv2019

Truth-preservation under fuzzy pp-formulas

How can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards this question, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint satisfaction. We study fuzzy positive-primitive sentences, and we present an algebraic characterization of classes axiomatized by this kind of sentences in terms of homomorphisms and direct products. The ultimate goal is to study the expressiveness and reasoning mechanisms of non-classical languages, with respect to constraint satisfaction problems and, in general, in modelling decision scenarios. fuzzy constraint satisfaction, fuzzy logics, model theory.

math.LO↗