Specifications with Observable Formulae and Observational Satisfaction Relation

We consider algebraic specifications with observational features. Axioms as well as observations are formulae of full (Many-Sorted) First Order Logic with Equality. The associated semantics is based on a non standard interpretation of equality called observational equality. We study the adequacy of this semantics for software specification and the relationship with behavioural equivalence of algebras. We show that this framework defines an institution. Keywords: algebraic specification, observability, semantics. 1 Introduction Within an observational approach the loose semantics of a specification may either be defined as a class of algebras observationally equivalent to models satisfying the specification in the usual sense or as a class of algebras observationally satisfying the specification. The former way has already been deeply explored in [13] while in the latter one, the following problems remains open: 1. How to define an observational satisfaction relation w.r.t. more sophis..