We present a technique that enables the use of finite model finding to check the satisfiability of certain formulas whose intended models are infinite. Such formulas arise when using the language of sets and relations to reason about structured values such as algebraic datatypes. The key idea of our technique is to identify a natural syntactic class of formulas in relational logic for which reasoning about infinite structures can be reduced to reasoning about finite structures. As a result, when a formula belongs to this class, we can use existing finite model finding tools to check whether the formula holds in the desired infinite model. 1

Abstract: This paper describes how to use an ontology for extensive semantic interrelation of documents in order to achieve sustainable development, i.e. continuous long-term usability of the contents. The ontology is structured via packages (corresponding to whole documents). Packages are related by import such that semantic interrelation becomes possible not only within a document but also between different documents. Coherence and consistency are enhanced by change management in a repository, including version control and configuration management. Semantic interrelation is realized by particular L ATEX commands for the declaration and definition of classes, objects and relations, and references to them, such that they can be used in standard L ATEX documents, in particular, with a new L ATEX style for educational material (slides, handouts, annotated courses, assignments, and so on). 1

As the first of two methodological devices aimed at increasing the trust in the `correctness' of a specification, we develop a calculus for proving consistency of Casl specifications. It turns out to be possible to delegate large parts of the proof load to syntactical criteria by structuring consistency proofs along the given specification structure, so that only in rather few remaining focus points, actual theorem proving is required. The practical usability of the resulting calculus is demonstrated by extensive examples taken from the Casl library of basic data types.

We introduce a semantic encoding of partial algebras as total algebras through a Horn axiomatization of the existence equality relation interpreted as an algebraic operation. We show that this novel encoding enjoys several important properties that make it a good tool for the execution of partial algebraic specifications through means specific to ordinary algebraic reasoning, such as term rewriting.

The goals of are CoFI WG are: to coordinate the completion of and disseminate the Common Framework; to demonstrate its practical applicability in industrial contexts; and to establish the infrastructure needed for future European collaborative research in algebraic techniques. We describe progress and activities in the first year of the project, 1 October 1998 -- 30 September 1999. 1 Progress Work in CoFI WG is carried out under six Task Groups. Progress and activities is each of these areas are described in the following subsections. 1.1 Language Design Casl version 1.0 has now been completed [25, 27]. Minor polishing of the design in the past year has not concerned the language proper but syntactic extensions for literals, some syntactic annotations concerning parsing and precedence of (mixfix) operator and predicate symbols, and semantic annotations for proof obligations arising from various kinds of conservative extensions [60]. Polishing the design has benefitted greatly ...

30 years have passed since the introduction by Joseph Goguen and Rod Burstall of the concept of ‘institution’ (in [14] under the name ‘language’). Since then institution theory has gradually developed from a simple and strikingly elegant general category theoretic formulation of the informal notion of logical system into an important trend of what is now called ‘universal logic’, with substantial

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We present a generic method for establishing interpolation properties by ‘borrowing ’ across logical systems. The framework used is that of the so-caled ‘institution theory ’ which is a categorical abstract model theory providing a formal definition for the informal concept of ‘logical system ’ and a mathematical concept of ‘homomorphism ’ between logical systems. We develop three different styles or patterns to apply the proposed borrowing interpolation method. These three ways are illustrated by the development of a series of concrete interpolation results for logical systems that are used in mathematical logic or in computing science, most of these interpolation properties apparently being new results. These logical systems include fragments of (classical many sorted) first order logic with equality, preordered algebra and its Horn fragment, partial algebra, higher order logic. Applications are also expected for many other logical systems, including membership algebra, various types of order sorted algebra, the logic of predefined types, etc., and various combinations of the logical systems discussed here. 1.