page 14 Declaration - page 15 Notes of copyright and the ownership of intellectual property rights - page 15 The Author - page 16 Acknowledgements - page 16 1 - Introduction - page 17 1.1 - Background - page 17 1.2 - The Style of Approach - page 18 1.3 - Motivation - page 19 1.4 - Style of Presentation - page 20 1.5 - Outline of the Thesis - page 21 2 - Models and Modelling - page 23 2.1 - Some Types of Models - page 25 2.2 - Combinations of Models - page 28 2.3 - Parts of the Modelling Apparatus - page 33 2.4 - Models in Machine Learning - page 38 2.5 - The Philosophical Background to the Rest of this Thesis - page 41 Syntactic Measures of Complexity - page 3 - 3 - Problems and Properties - page 44 3.1 - Examples of Common Usage - page 44 3.1.1 - A case of nails - page 44 3.1.2 - Writing a thesis - page 44 3.1.3 - Mathematics - page 44 3.1.4 - A gas - page 44 3.1.5 - An ant hill - page 45 3.1.6 - A car engine - page 45 3.1.7 - A cell as part of an organism -...

Abstract not found

Category theoretic models of information systems have by now been widely used in industrial consultancies (for some examples see [6] and [3]) and the models themselves have been developed in some detail in, for example, [4], [1], [10], [5], [11], [2] and [8]. Although many information systems are never meant to be implemented computationally (for example paper-based enterprise wide information models are frequently used by senior executives to help understand and plan the development of large corporations), the logic of an information system corresponds to the logic of the query language that might be used for interrogating the system (whether or not it is implemented). Typically this logic corresponds to a variation of predicate logic applied to simple finite domains. Most categorical information system modellers either avoid being explicit about the logic of their systems (thus acquiring the logic of whatever query language happens to be present in an implementation) or import the ...

s people in their characterizations of the situation. Nevertheless, several main threads can be identified, and one of the most evident is that one depicted in the figure: computational procedures began to operate on extremely rich data structures while databases tend to be more flexible and involved from the computational view point. In fact, to manage modern distributed information systems effectively one is forced to think in terms of semantically valid computational procedures, while classical computations over classical ADTs should be moved to the level of implementation. Such a setting seems to be close to the paradigm of object-orientation which is actively inculcated in both programming and database technology as well. Figure 1. The evolution of information technologies (IT) As for the Theory-line and its relations to PL and DB, the picture we present is much more speculative. It appears that in computation

. A graph-based specification language and the corresponding machinery are described as stating a basic framework for semantic modeling and database design. It is shown that a few challenging theoretical questions in the area, and some of hot practical problems as well, can be successfully approached in the framework. The machinery has its origin in the classical sketches invented by Ehresmann and is close to their generalization recently proposed by Makkai. There are two essential distinctions from Makkai's sketches. One consists in a different -- more direct -- formalization of sketches that categorists (and database designers) usually draw. The second distinction is more fundamental and consists in introducing operational sketches specifying complex diagram operations over ordinary (predicate) sketches, correspondingly, models of operational sketches are diagram algebras. Together with the notion of parsing operational sketches, this is the main mathematical contribution of the pape...