Behavioral equivalence of hidden k-logics: an abstract algebraic approach

This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the speci���cation and veri���cation of software systems. It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which di���erentiate visible and hidden sorts. Two main results of the paper are obtained by generalizing properties of the Leibniz congruence ��� the central notion in AAL. In this paper we discuss a question we posed in [1] about the relationship between the behavioral equivalences of equivalent hidden logics. We also present a necessary and su���cient intrinsic condition for two hidden logics to be equivalent.