In this paper we consider the partial many-sorted first-order logic and its extension to the subsorted partial many-sorted first-order logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not hold for these logics in general (i.e., with respect to arbitrary signature morphisms). Then we formulate conditions under which the generalization of the Craig Interpolation Property holds for the first logic.

The main aim of this paper is to present the completeness proof of a formal system for reasoning about logical consequences of structured specifications. The system is based on the proof rules for structural specifications build in an arbitrary institution as presented in [ST 88]. The proof of its completeness is inspired by the proof due to M. V. Cengarle (see [Cen 94]) for specifications in firstorder logic and the logical system for reasoning about them presented also in [Wir 91]. 1 Introduction In a number of papers on algebraic specifications (see [Cen 94, Far 92, ST 88, SST 92, Tar 86, Wir 91]) the main goal was to build: ffl a flexible enough specification formalism which allows one to cope with various problems of software engineering; ffl a sound and complete logic for reasoning about such specifications. We follow these goals when the first and a part of the second aim (soundness) is achieved by using structured specifications and the logical system built over an arbitrary...

Abstract. We show that any institution I satisfying some reasonable conditions can be transformed into another institution, Ibeh, which captures formally and abstractly the intuitions of adding support for behavioral equivalence and reasoning to an existing, particular algebraic framework. We call our transformation an “extension ” because Ibeh has the same sentences as I and because its entailment relation includes that of I. Many properties of behavioral equivalence in concrete hidden logics follow as special cases of corresponding institutional results. As expected, the presented constructions and results can be instantiated to other logics satisfying our requirements as well, thus leading to novel behavioral logics, such as partial or infinitary ones, that have the desired properties. 1

Acharacterization result for behaviorally de nable classes of hidden algebras shows that a class of hidden algebras is behaviorally de nable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically generalizes this result to a framework of any category with coproducts, a nal object and an inclusion system; this is general enough to include all coalgebra categories of interest. As a technical issue, the notions of equation and satisfaction are axiomatized in order to include the di erent approaches in the literature. 1

. Telecommunication systems involve many optional features which cannot be combined according to an obvious definition because they can interact together in an unpredictable way. In order to find the best way to combine features, a major di#culty is to foresee or to discover when a feature can disrupt an another one. Once such an interaction has been analysed, it still remains to define the best combination between the involved features. As this decision is purely subjective, we model the design of feature-oriented systems as an iterative process controlled by an expert judgement: all along the process, the expert increases his knowledge about the system under design and thus, may revise the feature integration design w.r.t. his expertise ... until he decides to accept the current feature integration as conform to his ideal view of the system. We propose to jointly adjust the description of a system built by integrating features and the expected properties on the global system all alon...

GB92] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality between morphisms and representations of institutions comes from an adjointness between categories of functors, and prove the cocompleteness of the categories of institutions over small signatures with morphisms and representations, respectively. Category: F.3, F.4

Generalizations of Craig interpolation are investigated for equational logic. Our approach is to do as much as possible at a categorical level, before drawing out the concrete implications.

New properties and implications of inclusion systems are investigated in the present paper. Many properties of lattices, factorization systems and special practical cases can be abstracted and adapted to our framework, making the various versions of inclusion systems useful tools for computer scientists and mathematicians.

. In practice, the formal development of software is an evolutionary process. Failed proof attempts give rise to changes in the speci cation and such changes invalidate proofs which have been previously performed. Clearly, it is very desirable to preserve much of the proof eort after such changes. In this paper, we propose development graphs as a general framework for modular specications and dene a structure preserving translation of Casl specications into these graphs. The feature of development graphs, which is most important for an evolutionary process, is that they simplify the analysis of changes to the specication such that their negative eects can be kept to a minimum. 1 Introduction It has long been recognized that specications in the large are only manageable if they are built in a structured way. Specication languages, like Casl [CASL98], provide various mechanisms to combine basic specications to structured specications. Analogously verication tools ha...

We show that for any behavioral Sigma-specification B there is an ordinary algebraic specification ~ B over a larger signature, such that a model behaviorally satisfies B if and only if it satisfies ~ B, where is the information hiding operator exporting only the Sigma-theorems of ~ B. The idea is to add machinery for contexts and experiments (sorts, operations and equations), use it, and then hide it. We develop a procedure, called unhiding, that takes a finite B and produces a finite ~ B. The practical aspect of this procedure is that one can use any standard equational or inductive theorem prover to derive behavioral theorems, even if neither equational reasoning nor induction is sound for behavioral satisfaction.