On the relationship between fuzzy description logics and many-valued modal logics

In this paper we study the relationships between a family of ALC-like fuzzy description logics (FDLs) defined over left-continuous t-norms and some many-valued multi-modal logics (MMLs). We analyze these relationships in both directions, that is, how to merge FDLs into MMLs and vice-versa. The analysis starts from the relationships between the languages to reach systematically the deeper level of reasoning tasks. At this level we are able to truly investigate both formalisms from each other point of view. Finally, the results concerning translations between reasoning tasks are applied in order to get decidability and complexity bounds.F. Esteva and À. García-Cerdaña acknowledge support from the Spanish MICINN project RASO TIN2015-71799-C2-1-P (MINECO/FEDER). À. García-Cerdaña also acknowledges support from the Spanish MICINN project Lógica algebraica y lógicas no clásicas ( MTM 2011-25747 ), and the grant 2014SGR-788 from the Generalitat de Catalunya . Esteva also acknowledges support via grant 2014SGR-118 from the Generalitat de Catalunya .Peer Reviewe