That IS-IN Isn't IS-A: A Further Analysis of Taxonomic Links in Conceptual Modelling
Jari Palomki, Hannu Kangassalo · Advances in Knowledge Representation · 2012
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 in its character. 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 example, by Brachman.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 conceptual modelling.www.intechopen.comAdvances in Knowledge Representation 4 The different meanings for the IS-A relationThe idea of IS-A relation seems to follow from the English sentences such as "Socrates is a man" and "a cat is a mammal", which provides two basic forms of using the IS-A relation.That is, a predication, where an individual (Socrates) is said to have a predicate (a man), and that one predicate (a cat) is said to be a subtype of the other predicate (a mammal).This second form is commonly expressed by the universally quantified conditional as follows: "for all entities x, if x is a cat, then x is a mammal".However, this formalization of the second use of the IS-A relation reveals, that it combines two commonly used expressions using the IS-A relation.Firstly, in the expressions of the form "x is a cat" and "x is a mammal" the IS-A relation is used as a predication, and secondly, by means of the universal quantifier and implication, the IS-A relation is used not as a predication, but as a connection between two predicates.Accordingly, we can divide the use of the IS-A relation in to two major subtypes: one relating an individual to a species, and the other relating two species.When analysing the different meanings for the IS-A relation Brachman uses this division by calling them generic/individual and generic/generic relations, (Brachman 1983, 32). Generic/individual relationsBrachman gives four different meanings for the IS-A relation connecting an individual and a generic, which we shall list and analyse as follows, (ibid.): How to referenceIn order to correctly reference this scholarly work, feel free to