Covering logics via possible-translations

Abstract

We present a general study of a new formalism of decomposition of logics, the Possible-Translations Coverings (in short PTC’s) which constitute a formal version of Possible-Translations Semantics, intro- duced by W. Carnielli in 1990. We show how the adoption of a more general notion of propositional signatures morphism allows us to de- fine a category Sig ω, in which the connectives, when translated from a signature to another one, enjoy of great flexibility. Essentially, Sig ω -morphisms will be multifunctions instead of functions. Using mor- phisms in Sig ω we define the notion of a PTC for a logic L. We ana- lyze some properties of PTC’s and give concrete examples of some of the above mentioned constructions. We conclude indicating the first steps to be followed in order to characterize PTC’s as a universal construction in an adequately defined category of logics.