Interval rough mereology and description logic: An approach to formal treatment of imprecision in the Semantic Web ontologies

Methods of symbolic computation in the presence of imprecision and uncertainty of information are important to many areas of computational mathematics. They are fundamentally important to the Semantic Web and generally important to other areas such as Artificial Intelligence. When fully realized, the Semantic Web will enable wide spread sharing and integration of machine stored information and software. Cornerstone of the Semantic Web is ontologies that describe domains of discourse and provide semantics to data. Ontologies identify important concepts in the domain and describe relationships between them. This is critical to achieving true machine understanding of Web’s resources. In the Semantic Web ontologies are often defined as formal logical structures that support intelligent machine processing. Current methodologies for representing ontologies do not provide sufficient support for managing imprecision. Defining ontologies is difficult for domains that contain imprecise knowledge, i.e. knowledge that cannot be represented by means of crisp logic and classical sets. Examples include uncertain, incomplete, vague and subjective knowledge. Computational methods such as reasoning with imprecise ontologies are not broadly provided. There is a critical need to have: first, a formal mathematical methodology for representing imprecise ontologies and second, formal methods for evaluating and computing with imprecise ontologies. Objective evidence for existence of this need is the extensive number of imprecise domains on the current Web that are not conceptualized in formal ontologies even though it is indispensable if success of the Semantic Web is to be fully achieved. Continuous existence of the need represents an important problem for the expansion of the Semantic Web because, until the need is met, many imprecise domains on the Web remain unavailable for machine exploration, understanding and computation.