Abstract. We present an institution of observational logic suited for state-based systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are required to be compatible with the indistinguishability relation determined by the given observers. In particular, we introduce a homomorphism concept for observational algebras which adequately expresses observational relationships between algebras. Then we consider a flexible notion of observational signature morphism which guarantees the satisfaction condition of institutions w.r.t. observational satisfaction of arbitrary first-order sentences. From the proof theoretical point of view we construct a sound and complete proof system for the observational consequence relation. Then we consider structured observational specifications and we provide a sound and complete proof system for such specifications by using a general, institution-independent result of [6]. 1

We consider observational specifications of state-based systems which incorporate the declaration of a distinguished set of observer operations. These observers determine an indistinguishability relation for states which is called "observational equality". An important requirement for the non-observer operations is the compatibility with the observational equality. In the CafeOBJ language (and in extended hidden algebra) this property is called "behavioural coherence". In this presentation we introduce the notion of an "observer complete definition" and we show that any (non-observer) operation which is defined using this pattern is behaviourally coherent. We also discuss some consequences of this result for relating observational logic and extended hidden algebra semantics and for proving the correctness of observational implementations.

This paper presents an (abstract) model theoretic semantics for ECLP, without directly addressing the computational aspect. This is a rather novel approach on the area of constraints where almost all efforts have been devoted to computational and operational issues; it is important the reader understands the model-theoretic and foundational orientation of this paper. However, we plan to gradually develop the computational side based on these foundations as further research (Section 7.2 sketches some of the directions of such further research). Some computational aspects of this theory can already be found in (Diaconescu, 1996c). This semantics is

This work describes the formal semantics of SCHEME 1 as an equational theory in the MAUDE rewriting system. The semantics is based on continuations and is highly modular. We briefly investigate the relationship between our methodology for defining programming languages and other semantic formalisms. We conclude by showing some performance results of the interpreter obtained for free from the executable specification.