Towards a Nonmonotonic Extension to OWL

We discuss ALCK, a nonmontonic logic that augments ALC with the epistemic operator K, and argue that a similar extension to OWL would be desirable. We show, however, that at its current state the OWL syntax is too inflexible to capture even this syntactically simpleminded extension. Finally, we introduce our implementation of ALCK as an extension to the tableau-based OWL-DL reasoner Pellet. 1 Nonmonotonic logics, open and closed worlds Nonmonotonic logics were proven generally successful in capturing, among other things, several forms of common sense and database reasoning. A bold divide between the field of nonmonotonic formalisms and first-order reasoning (where description logics and OWL lie) rests in the closed v. open world assumption. In database systems, it is reasonable to assume that the data at hand is complete. Since no information outside the database is relevant, we say that our world is closed. Formally, if Σ 6|= φ (where Σ is the knowledge in our database and φ is some formula), we assume ¬φ is the case. This constitutes the closed-world assumption (CWA). Under the open world assumption (OWA), on the other hand, it is accepted that the knowledge in our database is perhaps incomplete. When asked whether Σ |= φ, we simply come to no conclusion in case Σ 6|= φ and Σ 6|= ¬φ. We will not delve into the question of which semantics is “better” overall or more appropriate for OWL. Rather, we argue that it would be desirable to be able to “turn on” the closed-world assumption when needed in OWL, in order the reap the benefits of nonmonotonicity, but without giving up OWL’s openworld semantics in general. The logic ALCK allows for this interaction. Many useful nonmonotonic features such as integrity constraints and procedural rules (among others−we point to [1] for full treament) are formalizable in this logic. Consider as a motivational example for CWA, an integrity constraint. Suppose that for a certain application, we require all the employees in our knowledge base to be explictly declared to be either a manager or a programmer, since employees will be treated differently according to their positions. The subsumption axiom Employee v Manager t Programmer will not suffice, since an individual only declared to be an instance of Employee will trivially satisfy the disjunction even if it is not explcitly a member of either disjunct (so long as it is not in ¬Manager u ¬Programmer of course.) Thus the knowledge base Σ = {Employee(bob)} is a legitimate model of this concept, yet does not settle