Differences between ontology modeling approaches / Description Logic (DL) versus Higher-Order Logic

Differences between ontology modeling approaches / Description Logic (DL) versus Higher-Order Logic (HOL)

Ontologies are mainly known from the area of the Semantic Web. The Semantic Web uses the Web Ontology Language (OWL), whose various manifestations are essentially based on Description Logic (DL). The primary purpose of DL is to model domains, i.e., to describe concepts, roles, and instances, and represents a subset of First-Order Logic. A key feature of DL is that it follows the Open-World Assumption (OWA). The OWA is based on the assumption that an observer does not have complete knowledge about the world and therefore there are three logical states: true, false, and unknown. This approach is useful for a flexible and open information pool such as the Internet. However, for industrial applications (e.g., SQL), Close-Word Assumption has emerged as an economically preferable way to have complete information oversight for non-chaotic processes. For example, an airline must be able to rely on the fact that a passenger has not checked in if he or she has been assigned a seat and it is empty. When "reasoning" with OWL, this remains an open question. The common approach to remedy this with downstream so-called "closure axioms", (e.g. "man is not woman") would explode the modeling effort for the exemplary unoccupied seat.

Logic languages like Prolog, DataLog and especially the ObjectLogic used here are, in contrast to DL, complete programming languages (so-called "active ontologies"), with which one can model domains not only descriptively in their fixed factual contexts but also functionally. I.e., depending on internal or external states, factual contexts can also change, i.e., ontology functions can change the ontology, including the functions. This non-monotonic property of ObjectLogic is an essential requirement to implement semantic AI (see also on LPNMR - logic programming and non-monotonic reasoning).

An important criterion of a logic language is furthermore its expressivity and thus the economy of its use. HOL allows the formulation of sets of sets. The reasoning process over multi-level logics thus makes HOL very expressive.