On Finite-Valued Bimodal Logics with an Application to Reasoning About Preferences
In a previous paper by Bou et al., the minimal modal logic over a finite residuated lattice with a necessity operator \(\square \) was characterized under different semantics. In the general context of a residuated lattice, the residual negation \(\lnot \) 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 \(\Diamond \). 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.
KeywordsMany-valued modal logic Necessity and possibility modal operators Finite residuated lattice Reasoning about graded preferences
Vidal acknowledges support by the joint project Austrian Science Fund (FWF) I1897-N25 and Czech Science Foundation (GACR) 15-34650L, and by the institutional grant RVO:67985807. Esteva and Godo acknowledge support by the FEDER/MINECO project TIN2015-71799-C2-1-P.
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