A formalism for constructing and using axiomatic specifications in an arbitrary logical system is presented. This builds on the framework provided by Goguen and Burstall’s work on the notion of an institution as a formalisation of the concept of a logical system for writing specifications. We show how to introduce free variables into the sentences of an arbitrary institution and how to add quantitiers which bind them. We use this foundation to define a set of primitive operations for building specifications in an arbitrary institution based loosely on those in the ASL kernel specification language. We examine the set of operations which results when the definitions are instantiated in institutions of total and partial tirst-order logic and compare these with the operations found in existing specification languages. We present proof rules which allow proofs to be conducted in specifications built using the operations we define. Finally, we introduce a simple mechanism for defining and applying parameterised specifications and briefly discuss the program development process. 1 1988 Academic Press. Inc. 1.

Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. Viewpoints-based approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this paper, we propose a category-theoretic framework for the analysis of fuzzy viewpoints. Informally, a fuzzy viewpoint is a graph in which the elements of a lattice are used to specify the amount of knowledge available about the details of nodes and edges. By defining an appropriate notion of morphism between fuzzy viewpoints, we construct categories of fuzzy viewpoints and prove that these categories are (finitely) cocomplete. We then show how colimits can be employed to merge the viewpoints and detect the inconsistencies that arise independent of any particular choice of viewpoint semantics. We illustrate an application of the framework through a case-study showing how fuzzy viewpoints can serve as a requirements elicitation tool in reactive systems. 1

The purpose of a logical framework such as LF is to provide a language for defining logical systems suitable for use in a logic-independent proof development environment. All inferential activity in an object logic (in particular, proof search) is to be conducted in the logical framework via the representation of that logic in the framework. An important tool for controlling search in an object logic, the need for which is motivated by the difficulty of reasoning about large and complex systems, is the use of structured theory presentations. In this paper a rudimentary language of structured theory presentations is presented, and the use of this structure in proof search for an arbitrary object logic is explored. The behaviour of structured theory presentations under representation in a logical framework is studied, focusing on the problem of "lifting" presentations from the object logic to the metalogic of the framework. The topic of imposing structure on logic presentations...

This is an exploratory paper about combining logics, combining theories and combining structures. Typically when one applies logic to such areas as computer science, artificial intelligence or linguistics, one encounters hybrid ontologies. The aim of this paper is to identify plausible strategies for coping with ontological richness.

This paper presents axiomatizability results for Inclusive Equational Logic, a categorical generalization of equational logic that further generalizes local equational logic (Cazanescu 1993). The word "inclusive" is motivated by our pervasive use of inclusion systems, invented by Diaconescu, Goguen and Stefaneas (Diaconescu et al. 1993), and further developed in (Hilberdink 1996; Cazanescu and Rosu 1997); these are categories with extra structure to capture the notion of "inclusion". Inclusion systems can be very useful in computing science, e.g., in specification theory (Diaconescu et al. 1993)

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Rosetta is a speci cation language for designing hardware and software systems with a view to being able to consider multiple system perspectives concurrently (such as functional correctness, performance constraints, and physical constraints). It also provides the capability to integrate components from heterogeneous domains, such as software and recon- gurable systems and digital and analog hardware.

Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. This may result in inconsistencies between the descriptions provided by stakeholders. Viewpoints-based approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this thesis, we propose a category-theoretic framework for the analysis of fuzzy viewpoints. Informally, a fuzzy viewpoint is a graph in which the elements of a lattice are used to specify the amount of knowledge available about the details of nodes and edges. By defining an appropriate notion of morphism between fuzzy viewpoints, we construct categories of fuzzy viewpoints and prove that these categories are (finitely) cocomplete. We then show how colimits can be employed to merge the viewpoints and detect the inconsistencies that arise independent of any particular choice of viewpoint semantics. Taking advantage of the same category-theoretic techniques used in defining fuzzy viewpoints, we will also introduce a more general graph-based formalism that may find applications in other contexts. ii To my mother and father with love and gratitude. Acknowledgements First of all, I wish to thank my supervisor Steve Easterbrook for his guidance, support, and patience. I benefited from his advice throughout the entire course of this research, particularly so when exploring new ideas. His positive outlook and confidence in my work has always been a tremendous source of inspiration to me. I wish to thank Wolfram Kahl of the Department of Computing and Software at McMaster University for his invaluable help and constructive comments at different stages of my research. I am also indebted to him for taking up the responsibility of being the second reviewer of this thesis.

P. Bieber, P. Cros, P.Michel and V.Wiels Onera/Cert 2 Ave E. Belin, BP 4025 31055 Toulouse Cedex E-mail: fbieber,cros,michel,wielsg@cert.fr October 14, 1997 Introduction The main objective of this paper is to show how specification and implementation techniques studied at ONERA CERT can be used in order to develop rapidly and correctly distributed applications from off-the-shelf software components (or services). When already existing components are used to develop a distributed system, component heterogeneity might disrupt their correct interoperation. The independence of components providers is the main reason for this heterogeneity as each provider may use its favorite language to program the component or use a proprietary protocol to define how the component may interact with its environment. In this context, the first problem to be solved is to enable component interaction. But, even if components can interact together, they might still have a global behavior that is not correct....

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