Organizing Thematic, Geographic, and Temporal Knowledge in a Well-Founded Navigation Space: Logical and Algorithmic Foundations for EFGT Nets

We introduce a family of symbolic logical formalisms for reasoning with named entities, associated topics or thematic fields, geographic areas, and temporal periods. We argue that this kind of knowledge is useful for various applications in a Semantic Web context, in other words, for the content-oriented description of Web services and yellow pages. In our approach, entities and their relationships are positioned in a well-founded (i.e., acyclic) navigation space, called an EFGT Net. Large (small) entries regarding the navigation order represent general (specific) topics and large (small) geographic or temporal areas. This acyclic organization of knowledge aims to support indexing, search, and classification tasks directly. Each entry comes with a unique identifier that describes the role of the corresponding concept, using techniques from description logics. A formal semantics for the language of identifiers is given. For the resulting logic, role hierarchies and role-value maps are characteristic and crucial. Based on the semantics of identifiers, a set of intensionally typed links is defined that induces the aforementioned navigation structure on the set of all entries. We then introduce a set of deduction rules and a saturation procedure for computing all links between concepts, as well as intensional types for links. We prove soundness, completeness, and termination of the link derivation calculus.