In ordinary mathematics, an equation can be written down which is syntactically correct, but for which no solution exists. For example, consider the equation x = x + 1 defined over the real numbers; there is no value of x which satisfies it. Similarly it is possible to specify objects using the formal specification language Z [3,4], which can not possibly exist. Such specifications are called inconsistent and can arise in a number of ways. Example 1 The following Z specification of a functionf, from integers to integers "f x : ~ 1 x ~ O· fx = x + 1 (i) "f x : ~ 1 x ~ O· fx = x + 2 (ii) is inconsistent, because axiom (i) gives f 0 = 1, while axiom (ii) gives f 0 = 2. This contradicts the fact that f was declared as a function, that is, f must have a unique result when applied to an argument. Hence no suchfexists. Furthermore, iff 0 = 1 andfO = 2 then 1 = 2 can be deduced! From 1 = 2 anything can be deduced, thus showing the danger of an inconsistent specification. Note that all examples and proofs start with the word Example or Proof and end with the symbol.1.

The Z notation has been developed at the Programming Research Group at the Oxford University Computing Laboratory and elsewhere for over a decade. It is now used by industry as part of the software (and hardware) development process in both Europe and the USA. It is currently undergoing BSI standardisation in the UK, and has been proposed for ISO standardisation internationally. In recent years researchers have begun to focus increasingly on the development of techniques and tools to encourage the wider application of Z and other formal methods and notations. This volume contains papers from the Seventh Annual Z User Meeting, held in London in December 1992. In contrast to previous years the meeting concentrated specifically on industrial applications of Z, and a high proportion of the participants came from an industrial background. The theme is well represented by the four invited papers. Three of these discuss ways in which formal methods are being introduced, and the fourth presents an international survey of industrial applications. It also provides a reminder of the improvements which are needed to make these methods an accepted part of software development. In addition the volume contains several submitted papers on the industrial use of Z, two of which discuss the key area of safety-critical applications. There are also a number of papers related to the recently-completed ZIP project. The papers cover all the main areas of the project including methods, tools, and the development of a Z Standard, the first publicly-available version of which was made available at the meeting. Finally the volume contains a select Z bibliography, and section on how to access information on Z through comp.specification.z, the international, computer-based USENET newsgroup. Z User Workshop, London 1992 provides an important overview of current research into industrial applications of Z, and will provide invaluable reading for researchers, postgraduate students and also potential industrial users of Z.

This volume contains papers from the Eighth Z User Meeting, to be held at the University of Cambridge from 29 - 30 June 1994. The papers cover a wide range of issues associated with Z and formal methods, with particular reference to practical application. These issues include education, standards, tool support, and interaction with other design paradigms such as consideration of real-time and object-oriented approaches to development. Among the actual topics covered are: the formal specification in Z of Defence Standard 00-56; formal specification of telephone features; specifying and interpreting class hierarchies in Z; and software quality assurance using the SAZ method. Z User Workshop, Cambridge 1994 provides an important overview of current research into industrial applications of Z, and will provide invaluable reading for researchers, postgraduate students and also potential industrial users of Z.

The areas of active and real-time databases have seen a tremendous growth of interest in the past few years, particularly with regard to their support of time-critical and embedded applications. ARTDB-95 provided, therefore, an important forum for researchers from both communities to discuss research results, and also to chart new directions for the future. As well as the 11 submitted papers presented at the workshop, this volume also contains 4 invited papers on the following topics: the impact of active databases on commercial practice; the optimization of active database transactions; the need for better language, compiler and tool support for real-time databases; and the origin of time constraints associated with data, events and actions. Together the papers give a comprehensive overview of current research, and will provide invaluable reading for academic and industrial researchers and students at both undergraduate and postgraduate level.

This book is the proceedings of the Structures in Concurrency Theory workshop (STRICT) that was held from 11 th to l3th May 1995 in Berlin, Germany. It includes three invited contributions - by J. de Bakker, E. Best et aI, and E. R. Olderog and M. Schenke - and all papers which were submitted and accepted for presentation. Concurrency Theory deals with formal aspects of concurrent systems. It uses partly competing and partly complementary formalisms and structures. The aim of this workshop was to present and compare different formalisms and results in Concurrency Theory. STRICT was organized by the Humboldt-University Berlin and the ESPRIT Basic Research Working Group CALIBAN. Original papers had been sought from all scientists in the field of Concurrency Theory. The Programme Committee selected twenty contributions with various different topics, including Petri Nets, Process Algebras, Distributed Algorithms, Formal Semantics, and others. I am grateful to the Programme Committee and to the other referees for the careful evaluation of the submitted papers.

As the costs of power and timing become increasingly difficult to manage in traditional synchronous systems, designers are being forced to look at asynchronous alternatives. Based on reworked and expanded papers from the VII Banff Higher Order Workshop, this volume examines asynchronous methods which have been used in large circuit design, ranging from initial formal specification to more standard finite state machine based control models. Written by leading practitioners in the area, the papers cover many aspects of current practice including practical design, silicon compilation, and applications of formal specification. It also includes a state-of-the-art survey of asynchronous hardware design. The resulting volume will be invaluable to anyone interested in designing correct asynchronous circuits which exhibit high performance or low power operation.

The annual Irish Conferences on Artificial Intelligence and Cognitive Science have become the major forum in Ireland for the discussion of various aspects of artificial intelligence. Their aim is to provide a forum where researchers can present their current work, and where industrial and commercial users can relate this work to their own practical needs and experiences. Although the emphasis of the conferences is on Irish research, there are also important contributions from Europe, Australia, Canada, and the USA. This volume is based on the proceedings of the Fifth Irish Conference on Artificial Intelligence and Cognitive Science (AICS'92), which was held at the University of Limerick, Ireland, from 10-11 September 1992. The conference was divided into 6 sessions, covering knowledge representation, cognitive foundations, natural language 1 and 2, learning and expert systems, and nov§ el aspects of artificial intelligence and cognitive science. Because of the high number of papers submitted to the conference, a poster session was run in addition to the plenary sessions. Each paper presented at the poster session is represented in this volume by a four page abstract. Among the specific topics covered in this volume are: a model-based theory of conceptual combination; the nature and development of reasoning strategies; word recognition as a parsing problem; a knowledge-based autonomous vehicle system for emergency management support; the construction and use of scope neutral discourse entities; computer-based iconic communication; and exceptions in multiple inheritance systems. AI and Cognitive Science '92 provides a comprehensive record of current research into this important field. It will be of interest to researchers, lecturers and postgraduate students in a variety of disciplines related to artificial intelligence and cognitive science.

The last few years have borne witness to a remarkable diversity of formal methods, with applications to sequential and concurrent software, to real-time and reactive systems, and to hardware design. In that time, many theoretical problems have been tackled and solved, and many continue to be worked upon. Yet it is by the suitability of their industrial application and the extent of their usage that formal methods will ultimately be judged. This volume presents the proceedings of the first international symposium of Formal Methods Europe, FME'93. The symposium focuses on the application of industrial-strength formal methods. Authors address the difficulties of scaling their techniques up to industrial-sized problems, and their suitability in the workplace, and discuss techniques that are formal (that is, they have a mathematical basis) and that are industrially applicable. The volume has four parts: - Invited lectures, containing a lecture by Cliff B. Jones and a lecture by Antonio Cau and Willem-Paul de Roever; - Industrial usage reports, containing 6 reports; - Papers, containing 32 selected and refereedpapers; - Tool descriptions, containing 11 descriptions.

The Z notation has been developed at the Programming Research Group at the Oxford University Computing Laboratory and elsewhere for over a decade. It is now used by industry as part of the software (and hardware) development process in both Europe and the USA. It is currently undergoing BSI standardisation in the UK, and has been proposed for ISO standardisation internationally. In recent years researchers have begun to focus increasingly on the development of techniques and tools to encourage the wider application of Z and other formal methods and notations. This volume contains papers from the Seventh Annual Z User Meeting, held in London in December 1992. In contrast to previous years the meeting concentrated specifically on industrial applications of Z, and a high proportion of the participants came from an industrial background. The theme is well represented by the four invited papers. Three of these discuss ways in which formal methods are being introduced, and the fourth presents an international survey of industrial applications. It also provides a reminder of the improvements which are needed to make these methods an accepted part of software development. In addition the volume contains several submitted papers on the industrial use of Z, two of which discuss the key area of safety-critical applications. There are also a number of papers related to the recently-completed ZIP project. The papers cover all the main areas of the project including methods, tools, and the development of a Z Standard, the first publicly-available version of which was made available at the meeting. Finally the volume contains a select Z bibliography, and section on how to access information on Z through comp.specification.z, the international, computer-based USENET newsgroup. Z User Workshop, London 1992 provides an important overview of current research into industrial applications of Z, and will provide invaluable reading for researchers, postgraduate students and also potential industrial users of Z.

Database modelling is concerned with the design of reliable and efficient database systems. Three different approaches to modelling can be identified: structure-oriented, process-oriented, and behaviour-oriented. Database literature has traditionally focused on structure-oriented approaches, but it is now widely recognised that problems can be solved more effectively by integrating all three. As a result, modelling database dynamics is now considered to be as important as modelling static database structures. This volume contains selected papers from the Fourth International Workshop on Foundations of Models and Languages for Data and Objects, held in Volkse, Germany, 19-22 October, 1992. This series of international workshops was initiated by the Working Group on Foundations of Information Systems, part of the German Association for Informatics. It provides an international forum for the discussion of current research into database theory and its application to database technology. The theme of this particular workshop was modelling the dynamic behaviour of database systems in formal frameworks. As object-oriented principles are being widely used in current research work, particular emphasis was also given to object dynamics. Among the topics covered in this volume are: specifying the dynamics of complex objects databases; updates in a rule-based language for objects; an order-sorted approach to active objects; non-deterministic aspects of database transformations involving object creation; monitoring temporal permissions using partially evaluated transition graphs; a formalisation of logic databases and integrity constraints; a comparison of approaches for modelling dynamics of databases. Modelling Database Dynamics provides a comprehensive overview of current research into the modelling and use of database dynamics. It will provide invaluable reading for researchers, postgraduate students, and anyone interested in the theoretical foundations of computer science.