Description Logic vs. Order-Sorted Feature Logic

We compare and contrast Description Logic (DL) and Order-Sorted Feature (OSF) Logic from the perspective of using them for expressing and reasoning with knowledge structures of the kind used for the Semantic Web. Introduction The advent of the Semantic Web has spurred a great deal of interest in various Knowldege Representation formalisms for expressing, and reasoning with, so-called formal ontologies. Such ontologies are essentially sets of expressions describing data and properties thereof. Data is generally organized into ordered hierarchies of set-denoting concepts where the order denotes set inclusion. Properties are binary relations involving these concepts. This set-theoretic semantics is amenable to a crisp formal rendering based on first-order logic, and therefore to proof-theoretic operational semantics. Description Logic (DL) and Order-Sorted Feature (OSF) logic are two mathematical formalisms that possess such proof-theories. Both are direct descendants of Ron Brachman’s original ideas [1]. This inheritance goes through my own early work formalizing Brachman’s ideas [2], which in turn inspired the work of Gert Smolka, who pioneered the use of constraints both for the DL [3] and OSF [4] formalisms. While the DL approach has become the mainstream of research on the Semantic Web, the lesser known OSF formalisms have evolved out of Unification Theory [5], and been used in Constraint-Logic Programming and Computational Linguistics [6–19]. In this short communication (extracted from [20]), we compare and contrast DL and OSF logics with the purpose of using them effectively for ontological representation and reasoning. Relation between DL and OSF Formalisms The two formalisms for describing attributed typed objects of interest—viz., DL and OSF—have several common, as well as distinguishing, aspects. Thanks to both formalisms using the common language of FOL for expressing semantics, they may thus be easily compared—see, for example, [21, 22]. We here brush on some essential points of comparison and contrast. Common Aspects DL reasoning is generally carried out using (variations on) Deductive Tableau methods [23]. This is also the case of the constraint propagation rules of Fig. 1, which simply mimick a Deductive Tableau decision procedure [24]. OSF reasoning is performed by the OSF-constraint normalization rules of Figs. 2 and 3, which implement a logic of sorted-feature equality. 1 Due to severe, and strictly enforced, space limitation in these proceedings, most of the points we make here are further elaborated for the interested reader in [20]. 2 Although one can find some publications on Description Logics that do not (fully) use Tableaux reasoning for their operational semantics and mix it with resolution (i.e., Prolog technology), the overwhelming majority follow the official W3C recommendations based on Tableaux methods for TBox reasoning. 3 The constraint-rule notation we use is Plotkin’s SOS style [30]. The constraint system ALCNR is given here as an exemplar of a DL Tableaux-based reasoning system. It is neither the most expressive nor the most efficient. However, it uses the same style of formulaexpansion rules used by all Tableaux-based DL systems such as, in particular, the ever-growing family of esoterically-named Description Logics SHIQ, SHOIN , SHOIQ, SHOQ(D), SRIQ, and other SROIQ, which underlie all the official nocturnal bird languages promoted by the W3C to enable the Semantic Web—see for example the “official” DL site (http://dl.kr.org/) as well as the output of one of its most prolific spokesperson (http//www.cs.man.ac.uk/ ̃horrocks/Publications/). (C⊓) CONJUNCTIVE CONCEPT: