We extend the ordinary concept of theory morphism in institutions to extra theory morphisms. Extra theory morphism map theories belonging to different institutions across institution morphisms. We investigate the basic mathematical properties of extra theory morphisms supporting the semantics of logical multiparadigm languages, especially structuring specifications (module systems) a la OBJ-Clear. They include model reducts, free constructions (liberality), co-limits, model amalgamation (exactness), and inclusion systems. We outline a general logical semantics for languages whose semantics satisfy certain "logical" principles by extending the institutional semantics developed within the Clear-OBJ tradition. Finally, in the Appendix, we briefly illustrate it with the concrete example of CafeOBJ. Keywords Algebraic specification, Institutions, Theory morphism. AMS Classifications 68Q65, 18C10, 03G30, 08A70 2 1 Introduction Computing Motivation This work belongs to the research are...

. Ontologies allow the abstract conceptualisation of domains, but a given domain can be conceptualised through many different ontologies, which can be problematic when ontologies are used to support knowledge sharing. We present a formal account of ontologies that is intended to support knowledge sharing through precise characterisations of relationships such as compatibility and refinement. We take an algebraic approach, in which ontologies are presented as logical theories. This allows us to characterise relations between ontologies as relations between their classes of models. A major result is cocompleteness of specifications, which supports merging of ontologies across shared sub-ontologies. 1 Introduction Over the last decade ontologies --- best characterised as explicit specifications of a conceptualisation of a domain [17] --- have become increasingly important in the design and development of knowledge based systems, and for knowledge representations generally. They...

This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic category-based approach to a paramodulation-based operational semantics for equational logic programming languages. Category-based equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports i...

: Hyperprogramming is an emerging semantics-based technique for the integration of diverse features of programming environments, in particular, rapid prototyping and formal methods. This approach generalizes the notion of module to that of module cluster , which is an association around a central formal specification of various items of programming information, such as interface, source code, compiled code, rapid prototypes, formal proofs, test cases, performance estimates, documentation, history and accounting information. This allows all information items to be composed at the same time, by evaluating a master text called a module expression, which tells how to compose and transform module clusters. Hyperprogramming thus integrates design, specification, prototyping, coding, configuration, proof, testing, documentation and accounting into a single framework significantly generalizing both Ada generics and Unix 1 make. Hyperprogramming can also support a variety of different progra...

In this chapter we present some basic concepts and results of the theory of institutions, introduced by Goguen and Burstall to formally capture the informal notion of a logical system viewed from a model-theoretic perspective. We also sketch some possibilities of linking this to more proof-oriented concepts. We argue that the theory of institutions provides an appropriate framework for much of the work on formal software specification and development, as presented in this volume. Many standard logical systems used in particular versions of the algebraic specification paradigm may be viewed as institutions; some examples are given explicitly here, some others are hinted at. Developing (as much as possible) the ideas common to different versions of the algebraic specification paradigm in the framework of an arbitrary institution, and in particular providing a theory of formal specification and software development parameterized by an arbitrary institution rather than having a particular logical system built in, should be beneficial both by helping to avoid repetitious work and by bringing the concepts and results to an

This paper discusses an approach to software architecture based on concepts from parameterized programming, particularly its language of "module expressions." A module expression describes the architecture of a system as an interconnection of component modules, and executing the expression actually builds the system. Language features include: modules parameterized by theories, which declare interfaces; a number of module composition operations; views for binding modules to interfaces; and both vertical and horizontal composition. Modules may involve information hiding, theories may declare semantic restrictions with axioms, and views assert behavioral satisfaction of axioms by a module. Some "laws of software composition" are given, showing how various module composition operations are related. We also show how a variety of architectural styles can be supported, and how this approach can be extended to support evolution and traceability. All this is intended to ease the development of large systems, and in particular, to make reuse more effective in practice.

The fact that rewriting logic and Maude are reflective, so that rewriting logic specifications can be manipulated as terms at the metalevel, opens up the possibility of defining an algebra of module composition and transformation operations within the logic. This makes such a module algebra easily modifiable and extensible, enables the implementation of language extensions within Maude, and allows formal reasoning about the module operations themselves. In this paper we discuss in detail the Maude implementation of a specific choice of operations for a module algebra of this type, supporting module operations in the Clear/OBJ tradition as well as the transformation of object-oriented modules into system modules. 1

The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system used to write specifications, building on Goguen and Burstall's work on the notion of an institution as a formalisation of the concept of a logical system. One advantage of this is that it permits freedom in the choice of the logic used in writing specifications; an intriguing side-effect is that it enables Extended ML to be used to develop programs in languages other than Standard ML since we view programs as simply Extended ML specifications which happen to include only "executable" axioms. The semantics of Extended ML is defined in terms of the primitive specification-building operations of the ASL kernel specification language which itself has an institution-independent semantics. It is no...

This document describes FOOPS, an object-oriented specification language with an executable subset. The main distinguishing aspect of FOOPS is its advanced facilities for defining and interconnecting modules, which go beyond what other object-oriented languages offer. We present all the language features, explain their formal semantics, and provide a guide to its current implementation at Oxford.

this paper is to show how a collection of specification constructs may be formally defined that supports the former effort. We should stress that we shall not attempt to provide a full and practical specification language that can be used for object-oriented design. We shall have to limit ourselves to concentrate on the definition of our main primitive of specification (formalising the notion of object) together with two well known specification constructs: inheritance and aggregation (complex objects). However, we do not see deep problems in extending our results to other useful constructs such as class/type grouping and parameterisation.