Behavioral Institutions and Refinements in Generalized Hidden Logics

Manuel A. Martins (Aveiro University, Portugal)

Abstract: We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden k-logics) to the algebraic specification of object oriented programs. This is achieved through the Leibniz congruence relation and its combinatorial properties.

We reformulate the notion of hidden k-logic as well as the behavioral logic of a hidden k-logic as institutions. We define refinements as hidden signature morphisms having the extra property of preserving logical consequence. A stricter class of refinements, the ones that preserve behavioral consequence, is studied. We establish sufficient conditions for an ordinary signature morphism to be a behavioral refinement.

Keywords: Leibniz congruence, behavioral equivalence relation, behavioral logic, behavioral refinements, hidden logics, institutions, refinements

Categories: F.3.1, F.3.2, F.4.1