A formal language ccsl is introduced for describing specifications of classes in object-oriented languages. We show how class specifications in ccsl can be translated into higher order logic. This allows us to reason about these specifications. In particular, it allows us (1) to describe (various) implementations of a particular class specification, (2) to develop the logical theory of a specific class specification, and (3) to establish refinements between two class specifications. We use the (dependently typed) higher order logic of the proof-assistant pvs, so that we have extensive tool support for reasoning about class specifications. Moreover, we describe our own front-end tool to pvs, which generates from ccsl class specifications appropriate pvs theories and proofs of some elementary results.

. 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 paper is an introduction to recent research on hidden algebra and its application to software engineering; it is intended to be informal and friendly, but still precise. We first review classical algebraic specification for traditional "Platonic" abstract data types like integers, vectors, matrices, and lists. Software engineering also needs changeable "abstract machines," recently called "objects," that can communicate concurrently with other objects through visible "attributes" and state-changing "methods." Hidden algebra is a new development in algebraic semantics designed to handle such systems. Equational theories are used in both cases, but the notion of satisfaction for hidden algebra is behavioral, in the sense that equations need only appear to be true under all possible experiments; this extra flexibility is needed to accommodate the clever implementations that software engineers often use to conserve space and/or time. The most important results in hidden algebra are ...

Data Types and Algebraic Semantics The history of programming languages, and to a large extent of software engineering as a whole, can be seen as a succession of ever more powerful abstraction mechanisms. The first stored program computers were programmed in binary, which soon gave way to assembly languages that allowed symbolic codes for operations and addresses. fortran began the spread of "high level" programming languages, though at the time it was strongly opposed by many assembly programmers; important features that developed later include blocks, recursive procedures, flexible types, classes, inheritance, modules, and genericity. Without going into the philosophical problems raised by abstraction (which in view of the discussion of realism in Section 4 may be considerable), it seems clear that the mathematics used to describe programming concepts should in general get more abstract as the programming concepts get more abstract. Nevertheless, there has been great resistance to u...

: This paper outlines a research programme in algebraic engineering. It starts with a review of classical algebraic specification for abstract data types, such as integers, vectors, booleans, and lists. Software engineering also needs abstract machines, recently called "objects," that can communicate concurrently with other objects, and that have local states with visible "attributes" that are changed by inputs. Hidden algebra is a new development in algebraic semantics for such systems; its most important results are powerful hidden coinduction principles for proving behavioral properties, especially behavioral refinement. 1 Introduction In view of the title of this conference, I should confess to being an algebraic engineer in (perhaps) the following four different senses: 1. I use algebra to build real software systems. 2. I build huge algebras to help build software systems. 3. I build software tools to help deal with these huge algebras. 4. I build new kinds of algebra, to get be...