@inproceedings { 5613, title = {On finite-valued bimodal logics with an application to reasoning about preferences}, booktitle = {Advances in Fuzzy Logic and Technology, Proc. of EUSFLAT 2017}, volume = {643}, year = {2018}, month = {11/09/2017}, pages = {505-517}, publisher = {Springer AC}, organization = {Springer AC}, edition = {J. Kacprzyk et al.}, address = {Warsaw}, abstract = {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.}, URL = {https://link.springer.com/chapter/10.1007%2F978-3-319-66827-7_47}, author = {Amanda Vidal and Francesc Esteva and Llu\'{\i}s Godo} }