TitleOn finite-valued bimodal logics with an application to reasoning about preferences
Publication TypeConference Paper
Year of Publication2018
AuthorsVidal A, Esteva F, Godo L
Conference NameAdvances in Fuzzy Logic and Technology, Proc. of EUSFLAT 2017

In a previous paper by Bou et al., the minimal modal logic over a finite residuated lattice with a necessity operator \Box 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 Q. 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.