|Title||On finite-valued bimodal logics with an application to reasoning about preferences|
|Publication Type||Conference Paper|
|Year of Publication||2018|
|Authors||Vidal A, Esteva F, Godo L|
|Conference Name||Advances 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.
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