In this paper we propose a very general de nition of combination
of logics by means of the concept of sheaves of logics.
We first discuss some properties of this general definition 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 first 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