Axiomatizing logics of fuzzy preferences using graded modalities

09/17/2019

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by   Amanda Vidal, et al.

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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 and define appropriate extensions on a multi-modal language with graded modalities, both for weak and strict preferences. 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.