A semantic approach to interpolation

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss someapplications of our results to the theory of institutions and of algebraic specifications,and a Craig-Robinson version of these results

A semantic approach to interpolation

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss someapplications of our results to the theory of institutions and of algebraic specifications,and a Craig-Robinson version of these results

A short overview of Hidden Logic

In this paper we review a hidden (sorted) generalization of k-deductive systems - hidden k-logics. They encompass deductive systems as well as hidden equational logics and inequational logics. The special case of hidden equational logics has been used to specify and to verify properties in program development of behavioral systems within the dichotomy visible vs. hidden data. We recall one of the main applications of this work - the study of behavioral equivalence. Related results are obtained through combinatorial properties of the Leibniz congruence relation. In addition we obtain a few new developments concerning hidden equational logic, namely we present a new characterization of the behavioral consequences of a theory