Inheritance in Hierarchical Relational Structures

Inheritance in Hierarchical Relational Structures Derek P. LONG Dept. of Computer Science, University College London, Gower Street, London, ENGLAND. Roberto GARIGLIANO School of Engineering and Applied Science, University of Durham, Durham, ENGLAND. Abstract A brief survey is conducted of the inheritance principle - the conveyance of properties between components within a hierarch- ical relational structure. The standard form of inheritance is con- sidered, using the subset (is-a) relation and highlighted as an example of downward inheritance. Downward inheritance is extended to specialisation of actions, and cases are presented in which the rule fails. sider them on tile same plane of generality and abstractness as the standard hierarchical inheritance rules. Upward inheritance, on the other hand, is formally on the same plane as the more common downward form. Our analysis shows that the explana- tion for this powerful tool resides in one semantical aspect of a large class of very common relations. 2. Downward inheritance An alternative and less well-known form of inheritance is intro- duced - upward inheritance. Several examples in which upward inheritance is valid and others in which it is not valid are given, in a treatment highlighting the analogy with downward inheri- tance. The validity of the rule, in those case in which it operates, is underlined, to distinguish it from induction. A brief acconnt is given of tile search for the underlying reasons for the validity of inheritance rules and these are then given. The solution turns out to be due to a hidden or implicit quantifier within the relations that are used. The semantical nature of the problem and of its solution are stressed, emphasis- ing the impossibility of a purely syntactic analysis and solution to the problem. Various points of interest arising from the analysis ,are listed and discussed. 1. Introduction The use of structures for representing knowledge has long been acknowledged as a vital tool in AI. A consequence of the use of structures is the identification of certain kinds of hierarchically organised sub-structures. These have many useful purposes, but one of particular significance is that of avoiding repetition, by storing information at one place in the hierarchy, and then using the hierarchical structure to infer that the property is inherited by many other components of the structure. In addition to the savings in storage that this inheritance over hierarchies can offer, there is the possibility of using the hierarchy to infer new infor- mation, so that the process becomes not just a means of saving space, but also of generating new knowledge. The form of inheritance most frequently studied is what we call "downward inheritance", because it exploits the passage from the general to the particular. There has been a considerable amount of work done about inheritance between objects via total inclu- sion relations, for the very good reason that this form is always valid /Findler 1979/. This form is sometimes confused with downward inheritance betwen sets, which, as we briefly discuss below, is much more problematic. We will concentrate on total …

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