On Possible Applications of Rough Mereology to Handling Granularity in Ontological Knowledge

Representing and reasoning about knowledge is critical in Artificial Intelligence. There is a distinction between factual and ontological knowledge. Factual knowledge represents a set of facts about individual objects that are known or believed whereas ontological (background) knowledge represents implicit concepts and relationships that are assumed to exist in the world. Ontological knowledge is often represented as a hierarchy of concepts because splitting things of the real world into categories and sub-categories is a natural way of human thinking. One example of conceptual hierarchies in AI is ontologies that are widely used in such areas as Natural Language Processing, Semantic Web, etc. Representation of both types of knowledge becomes difficult when the knowledge is imprecise. One example of imprecision is granularity i.e. inability to distinguish between the individual objects. In this case, knowledge cannot be represented precisely but can be approximated with respect to the granularity of the domain. Approximation of factual knowledge has been extensively researched and often employs Rough Set Theory (Pawlak 1982) for dealing with indiscernibility of objects. Similar approach has been applied to ontologies to approximate concepts in the hierarchy (Doherty et al. 2003). The open problem is the approximations of hierarchical relationships (such as ”is-a”, ”part-of”) between concepts. This paper addresses this issue using Rough Mereology (Polkowski & Skowron 1996) complemented with Interval Analysis (Moore 1966). The principal contribution is to provide rough mereological functions that can be used for representation and reasoning with formal ontologies in approximation spaces. Specifically, approximate concept membership and approximate concept subsumption functions will be provided. It can be demonstrated that the interval based functions are free of the shortcomings of the previously suggested definitions (Cao, Sui, & Zhang 2003) (Klinov & Mazlack 2007).