**Section 1**

**On Foundations** 

**1** 

**That IS-IN Isn't IS-A: A Further Analysis** 

Jari Palomäki and Hannu Kangassalo

*University of Tampere* 

*Finland* 

**of Taxonomic Links in Conceptual Modelling** 

Ronald J. Brachman, in his basic article: "What IS-A Is and Isn't: An Analysis of Taxonomic Links in Semantic Networks", (1983), has analysed and catalogued different interpretations of inheritance link, which is called "IS-A", and which is used in different kind of knowledge-representation systems. This IS-A link is seen by Brachman as a relation "between the representational objects," which forms a "taxonomic hierarchy, a tree or a lattice-like structures for categorizing classes of things in the world being represented", (ibid., 30). This very opening phrase in Brachman's article reveals, and which the further analysis of his article confirms as it is done in this Chapter, that he is considering the IS-A relation and the different interpretations given to it as an *extensional* relation. Accordingly, in this Chapter we are considering an *intensional* IS-IN relation which also forms a taxonomic hierarchy and a lattice-like structure. In addition, we can consider the hierarchy provided by an IS-IN relation as a semantic network as well. On the other hand, this IS-IN relation, unlike IS-A relation, is a conceptual relation between concepts, and it is basically intensional

The purpose of this Chapter is to maintain that the IS-IN relation is not equal to the IS-A relation; more specifically, that Brachman's analysis of an extensional IS-A relation did not include an intensional IS-IN relation. However, we are not maintaining that Brachman's analysis of IS-A relation is wrong, or that there are some flaws in it, but that the IS-IN relation requires a different analysis than the IS-A relation as is done, for

This Chapter is composed as follows. Firstly, we are considering the different meanings for the IS-A relation, and, especially, how they are analysed by Brachman in (1983), and to which, in turn, we shall further analyse. Secondly, we are turning our attention to that of the IS-IN relation. We start our analysis by considering what the different senses of "in" are, and to do this we are turning first to Aristotle's and then to Leibniz's account of it. After that, thirdly, we are proceeding towards the basic relations between terms, concepts, classes (or sets), and things in order to propose a more proper use of the IS-IN relation and its relation to the IS-A relation. Lastly, as kind of a conclusion, we are considering some advances and some difficulties related to the intensional versus extensional approaches to a

**1. Introduction** 

in its character.

example, by Brachman.

conceptual modelling.
