A Categorial Approach to the Combination of Logics1

In this paper we propose a very general deenition of combination of logics by means of the concept of sheaves of logics. We rst discuss some properties of this general deenition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the rst author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. 1 Partly nanced by CAPES and DAAD (PROBRAL project involving the Universities of Campinas (Brazil) and Karlsruhe (Germany)). The rst author also acknowledges nancial support from CNPq (Brazil) and from the Advanced Reasoning Forum. We thank Richard L. Epstein and Jo~ ao Marcos for a careful reading of this paper.