Possible-translations Algebraizability

The interest of investigating combinations of logics has a philosophical side, a purely logic-theoretical side and promising applicational interests. This paper concentrates on the logic-theoretical side and studies some general methods for combination and decomposition, taking into account that the general idea of combining logics requires methods not only for building new logics, but also for breaking logics into families of logics with lower semantical complexity. The possible-translations semantics, introduced in [8] and subsequently refined, is a particularly apt tool for analyzing and providing semantical meaning and algebraic contents to certain complex logics as paraconsistent logics, and this paper characterizes the possibletranslations semantics (PTS) and the concept of algebraizability via a PTSs in categorial terms, showing that the product of finitely-algebraizable (or Blok-Pigozzi algebraizable) propositional logics is also finitely-algebraizable, under certain very reasonable conditions. Examples and some research directions are discussed.