Formal reasoning is notoriously long and arduous; in order to use it to reason effectively in the construction of programs it is, therefore, paramount that we design our notations to be both clear and economical. Taking examples from AI, from imperative programming, from the use of the Bird-Meertens formalism and from category theory we demonstrate how the right choice of what to denote and how it is denoted can make significant improvements to formal calculations. Brief mention is also made of the connection between economical notation and properties of type. 1 2 Foreword Earlier this year I was an invited speaker at the 5th British Computer Society Theoretical Computer Science Colloquium held at Royal Holloway and Bedford New College, London. Before you is the text of my lecture, almost but not quite as given at the conference. (Perhaps the best way to describe the present paper is as the lecture that I should have given.) The publication of the text of the lecture will, ...

For succesful information systems development, conceptual data modelling is essential. Nowadays many techniques for conceptual data modelling exist, examples are NIAM, FORM, PSM, many (E)ER variants, IFO, and FDM. In-depth comparisons of concepts of these techniques is very difficult as the mathematical formalisations of these techniques, if existing at all, are very different. As such there is a need for a unifying formal framework providing a sufficiently high level of abstraction. In this paper the use of category theory for this purpose is addressed. Well-known conceptual data modelling concepts are discussed from a category theoretic point of view. Advantages and disadvantages of the approach chosen will be outlined. Keywords: Conceptual Data Modelling, Category Theory, Meta Modelling Classification: 68P99 (AMS-1991), H.1.0. (CR-1991) 1 Introduction It seems an undisputed fact that, opposed to most mature scientific disciplines, the discipline of information systems does not hav...

For successful information systems development, conceptual data modeling is essential. Nowadays a plethora of techniques for conceptual data modeling exist. Many of these techniques lack a formal foundation and a lot of theory, e.g. concerning updates or schema transformations, is highly data model specific. As such there is a need for a unifying formal framework providing a sufficiently high level of abstraction. In this paper the use of category theory for this purpose is addressed. Well-known conceptual data modeling concepts, such as relationship types, generalization, specialization, and collection types are discussed from a categorical point of view. An important advantage of this framework is its "configurable semantics". Features such as null values, uncertainty, and temporal behavior can be added by selecting appropriate instance categories. The addition of these features usually requires a complete redesign of the formalization in traditional set-based approaches to semantics...

For successful information systems development, conceptual data modeling is essential. Nowadays many techniques for conceptual data modeling exist. In-depth comparisons of concepts of these techniques are very difficult as the mathematical formalizations of these techniques, if they exist at all, are very different. As such there is a need for a unifying formal framework providing a sufficiently high level of abstraction. In this paper the use of category theory for this purpose is addressed. Well-known conceptual data modeling concepts, such as relationship types, generalization, specialization, collection types, and constraint types, such as the total role constraint and the uniqueness constraint, are discussed from a categorical point of view. An important advantage of this framework is its "configurable semantics". Features such as null values, uncertainty, and temporal behavior can be added by selecting appropriate instance categories. The addition of these features usually requir...

this paper is an alternative to diagram chasing (4). The use of a standard notation for various unique arrows obviates in some cases the need for pictures for the purpose of naming (2). The need for a pictorial overview of the typing (1) is decreased to some extend by a consistent notation, in particular f ; g for composition (so that f : a ! b g: b ! c ) f

Although the need for formalisation of modelling techniques is generally recognised, not much literature is devoted to the actual process involved. This is comparable to the situation in mathematics where focus is on proofs but not on the process of proving. This paper tries to accomodate for this lacuna and provides essential principles for the process of formalisation in the context of modelling techniques as well as a number of small but realistic formalisation case studies.