Analysing Analogy

Analogical reasoning is one of the most important techniques used by people, yet it has proved very difficult to represent the process in formal terms amenable to operational implementation in computer algorithms. In this paper we analyse the concept of an analogy and its application to reasoning processes. An analogy is seen to be a partial correspondence between two sYstems. In representing it in map-theoretic terms a third system naturally arises which may be injected into each of the others to represent the part lal correspondence. This system may be called an 'analogy' system capturing the particular analogy under consideration. We then go on to consider multiple analogies between two systems and their inter-relationships and show that these form a semi-lattice with a truth-system as the minimal element. Because analogies are between systems with structure they have to capture the transformations that define the structure rather than just the elements of the systems. Hence the systems themselves are most simply represented as categories and the mappings as faithful fun(".tors between them. In this paper we give not only the formal theory but a number of systemic and programming examples to illustrate our analysis.