On Finite-Valued Bimodal Logics with an Application to Reasoning About Preferences

Authors: Amanda Vidal, F. Esteva, L. Godo
Publication year: 2018
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Advances in Fuzzy Logic and Technology 2017
Projects: Modeling vague quantifiers in mathematical fuzzy logic
Bibliographic citation: VIDAL, Amanda, ESTEVA, F., GODO, L. On Finite-Valued Bimodal Logics with an Application to Reasoning About Preferences. In: KACPRZYK, J., SZMIDT, E., ZADROZNY, S., ATANASSOV, K.T., KRAWCZAK, M., eds. Advances in Fuzzy Logic and Technology 2017. Vol. 3. Cham: Springer, 2018, S. 505-517. Advances in Intelligent Systems and Computing, 643. ISBN 978-3-319-66826-0. ISSN 2194-5357
Dostupné z: doi:10.1007/978-3-319-66827-7_47
DOI: 10.1007/978-3-319-66827-7_47
ID: 478659

Abstract

In a previous paper by Bou et al., the minimal modal logic over a finite residuated lattice with a necessity operator was characterized under different semantics. In the general context of a residuated lattice, the residual negation is not necessarily involutive, and hence a corresponding possibility operator cannot be introduced by duality. In the first part of this paper we address the problem of extending such a minimal modal logic with a suitable possibility operator. In the second part of the paper, we introduce suitable axiomatic extensions of the resulting bimodal logic and define a logic to reason about fuzzy preferences, generalising to the many-valued case a basic preference modal logic considered by van Benthem et al.