Behavioural theories are a generalization of first-order theories where the equality predicate symbol is interpreted by a behavioural equality of objects (and not by their identity). In this paper we first consider arbitrary behavioural equalities determined by some (partial) congruence relation and we show how to reduce the behavioural theory of any class of algebras to (a subset of) the standard theory of some corresponding class of algebras. This reduction is the basis of a method for proving behavioural theorems whenever an axiomatization of the behavioural equality is provided. Then we focus on the important special case of (partial) observational equalities where two elements are observationally equal if they cannot be distinguished by observable computations over some set of input values. We provide general conditions under which an obvious infinite axiomatization of the observational equality can be replaced by a finitary one and we provide methodological guidelines for finding such...

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. Fully concurrent models of distributed object systems are specified using linear temporal logic that does not per se cope with concurrency. This is achieved by employing the principle of local sequentiality: we specify from local viewpoints assuming that there is no intraobject concurrency but full inter-object concurrency. Local formulae are labelled by identity terms. For interaction, objects may refer to actions of other objects, e.g., calling them to happen synchronously. A locality predicate allows for making local statements about other objects. The interpretation structures are global webs of local life cycles, glued together at shared communication events. These interpretation structures are embedded in an interpretation frame that is a labelled locally sequential event structure. Two initiality results are presented: the category of labelled locally sequential event structures has initial elements, and so has the full subcategory of those satisfying given temporal axioms. As...

We examine a variety of liberal logical frameworks of partial algebras. Therefore we use simple, conjunctive and weak embeddings of institutions which preserve model categories and may map sentences to sentences, finite sets of sentences, or theory extensions using unique existential quantifiers, respectively. They faithfully represent theories, model categories, theory morphisms, colimit of theories, reducts etc. Moreover, along simple and conjunctive embeddings, theorem provers can be re-used in a way that soundness and completeness is preserved. Our main result states the equivalence of all the logical frameworks with respect to weak embeddability. This gives us compilers between all frameworks. Thus it is a chance to unify the different branches of specification using liberal partial logics. This is important for reaching the goal of formal interoperability of different specification languages for software development. With formal interoperability, a specification can contain part...

Starting from the principle of software reusability through formal specifications we suggest a model for the retrieval of reusable components utilizing the search techniques in database management systems. The formal specification language of software components is ASL. Component specifications will be translated into a specification written in the knowledge representation language Telos for storage and other manipulation. The retrieval of software components is based on signature matching between the signatures of goal specifications and those of reusable components. In this way, we overcome some of the main problems with respect to retrieval such as representation of reusable components, representation of goal specification, and name differences in the software. The retrieval mechanism is supported by the Database Management System ConceptBase. 1 Introduction Software reusability serves two purposes: one is to reduce the costs of software development, and the other is to enhance th...

Higher-order logic with shallow type class polymorphism is widely used as a specification formalism. Its polymorphic entities (types, operators, axioms) can easily be equipped with a ‘naive ’ semantics defined in terms of collections of instances. However, this semantics has the unpleasant property that while model reduction preserves satisfaction of sentences, model expansion generally does not. In other words, unless further measures are taken, type class polymorphism fails to constitute a proper institution, being only a so-called rps preinstitution; this is unfortunate, as it means that one cannot use institution-independent or heterogeneous structuring languages, proof calculi, and tools with it. Here, we suggest to remedy this problem by modifying the notion of model to include information also about its potential future extensions. Our construction works at a high level of generality in the sense that it provides, for any preinstitution, an institution in which the original preinstitution can be represented. The semantics of polymorphism used in the specification language HasCasl makes use of this result. In fact, HasCasl’s polymorphism is a special case of a general notion of polymorphism in institutions introduced here, and our construction leads to the right notion of semantic consequence when applied to this generic polymorphism. The appropriateness of the construction for other frameworks that share the same problem depends on methodological questions to be decided case by case. In particular, it turns out that our method is apparently unsuitable for observational logics, while it works well with abstract state machine formalisms such as state-based Casl.

The goal of this paper is to explain the usage and semantics of hierarchical defaults in logical specifications. We discuss the usefulness of defaults for different specification scenarios like specialization, aggregation, explanation, revision, etc. To understand defaults formally, we introduce a general framework parameterized on the underlying logical institution extended by an instantiation mechanism for formulae. It is shown that hierarchical defaults have intended models if the extended institution is compact. As an example for a non-standard logic, we give the semantics of defaults in the multi-modal object calculus of the is-core project. To structure and compose specifications with defaults, default-preserving specification morphisms are defined and corresponding colimit constructions are sketched. 1 Introduction In this paper, we want to explain the usage and semantics of defaults in logic-based system specifications, particularly in specifications having an object-oriented ...

. We provide a mathematical specification of an extension of Warren's Abstract Machine for executing Prolog to type-constraint logic programming and prove its correctness. Our aim is to provide a full specification and correctness proof of a concrete system, the PROTOS Abstract Machine (PAM), an extension of the WAM by polymorphic order-sorted unification as required by the logic programming language PROTOS-L. In this paper, while leaving the details of the PAM's type constraint representation and solving facilities to a sequel to this work, we keep the notion of types and dynamic type constraints abstract to allow applications to different constraint formalisms like Prolog III or CLP(R). This generality permits us to introduce modular extensions of Borger's and Rosenzweig's formal derivation of the WAM. Since the type constraint handling is orthogonal to the compilation of predicates and clauses, we start from type-constraint Prolog algebras with compiled AND/OR structure that are der...

We provide a semantic basis for heterogeneous specifications that not only involve different logics, but also different kinds of translations between these. We show that Grothendieck institutions based on spans of (co)morphisms can serve as a unifying framework providing a simple but powerful semantics for heterogeneous specification.

this paper, we will describe the main techniques for the semantic definition of some of the most used structuring and modular constructs. Our main aim will be to study the generic, "institutionindependent ", version of each construct. However, in order to provide intuition, in most cases, we will first study these constructions in connection to equational logic.