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How do users use OWL and RIF together? When should they use one or the other or both?

The WG is chartered to produce a Rec-track deliverable on this topic. It will probably address RDF Compatibility as well.

During the F2F1 Breakout Session on OWL and RDF Compatibility there was general agreement that the approaches to using OWL with RIF should be enumerated, although we should also try to keep the list short.

Barriers to Compatibility

Incorporating OWL DL and Horn rules has several problems. However, considering only OWL DL does eliminate all the issues with RDF and RDFS meta-modelling.

Equality in OWL

OWL has a built-in notion of equality. This shows up in both owl:sameAs and number restrictions. The notion of equality from OWL is difficult to reconcile with treatments of rules that use the Herbrand universe, as the Herbrand universe has an immutable notion of equality. Employing either of the rule meanings that employ the Herbrand base would require, to start, making a global unique names assumption.

Disjunction in OWL

OWL has several forms of disjunctive constructs, including existential restrictions over enumerated classes, such as

There is no single minimal model for this KB and thus combinations of rules and OWL will not have single minimal models.

This lack of minimal models for OWL cannot be remedied by using a form of Skolemization, as was done for blank nodes in axioms. There is no way that a skolem constant can be added to the Herbrand base in the example above, as it would be different from the only two instances of foo, but would have to be an instance of foo.

Herbrand universe and OWL

In the meanings for rules based on the Herbrand universe, the domain of discourse is the Herbrand universe, and no more. This causes several problems.

First, it is possible to have a predicate accidentally be true on the entire universe, as in

This would have the unusual consequence that owl:Thing is a subclass of p, i.e.,

Second, potential values for implicit existentials in OWL have to belong to this universe, which causes problems like


as a is the only element of the domain of discourse.

Note as well, that this causes a weird kind of non-monotonicity, as

does not imply

but instead implies

Negation in OWL

However, the biggest problem in combining some meanings of rules and OWL is that OWL has negation. In the presense of negation, the meanings above based on minimal models differ from the first-order meaning.

Consider, for example,

Under any of the minimal model semantics above, the would entail


would imply

Note that the above examples show a standard form of non-monotonicity, as, in particular

does not entail

Approaches to Compatibility

As we can see from the barriers outlined above, the combination of OWL DL with rules (under the usual minimal model semantics) is not straight-forward. In the following we refer to rules interpreted under the minimal model semantics as LP rules.

We distinguish three approaches to achieving compatibility between OWL DL and LP rules, namely the superset, subset and blackbox approaches.

Superset Approach

The superset approach assumes a formalism which can capture the semantics of both an expressive Description Logic (OWL DL) and LP rules. There are several nonmonotonic logics which are candidates for such a formalism, such as circumscription, autoepistemic logic and default logic. In fact, there is an approach of extending Description Logics with epistemic operators, proposed by Donini and others from Rome (1). This approach could be extended to include LP rules.

There are several challenges in this approach. Several representational issues need to be overcome. Extending nonmonotonic logics to allow non-unique names and unnamed individuals, which are both allowed in OWL DL, is a challenging problem. Although there are several proposals to overcome some of these issues, it is by no means a solved problem. Furthermore, it is in general computationally very hard to deal with nonmonotonic logics and there are very few reasoners available. Combining classical logics and Logic Programming in a nonmonotonic formalism is an ongoing research topic (2) and, in our opinion, not suitable for standardization.

Subset Approach

A subset of OWL DL, the Horn logic subset, can be translated to LP rules. The result of this translation is called DLP (Description Logic Program); see (3). This translation preserves the ground consequences of the ontology; non-ground consequences are not defined for LP-rules. It is now straight-forward to add LP rules to the result of the translation.

A major disadvantage of this approach is that only a certain class of OWL DL ontologies can be translated to LP rules. In particular, axioms which involve equality, existential quantification, or disjunction in the consequent (i.e., right-hand side of the subsumption relation) cannot be translated. This means that either ontologies which contain such axioms cannot be translated or such axioms would be disregarded in the translation and would be lost. Several extensions of the translation have been investigated to allow additional features such as equality and existential quantification (see e.g. (4) and (5)), but it will not be possible to cover all features of OWL DL in the LP rules world.

The major advantage of this approach is that existing rule reasoners can be readily used to reason with the DLP ontology and the LP rules which are added to it. Many reasoners on the Semantic Web are based on LP rules and thus we may expect easy adoption by the users of these reasoners.

Black box Approach

In the black box approach, OWL DL and the LP rules are viewed as black boxes which exchange only ground facts. This approach was first investigated in the course of AL-Log and later refined to Eiter et al's "dl-programs" (6).

The body of an LP rule may contain queries to the OWL DL ontology which are taken into account in the evaluation of the LP rules. Additionally, ground facts may be sent to the OWL DL ontology before executing the query.

The advantage of this approach is that it is reasonably well understood and it allows to use all of OWL DL, rather than a subset. The other main advantage is that the approach allows to reuse existing OWL DL reasoners and that LP rule reasoners only need a relatively small adaptation to be able to query the DL reasoner.

The approach also has a number of disadvantages. First of all, it is not possible to reuse any of the equality information in the OWL DL ontology, although it is possible to imagine extensions of the dl-programs approach with a limited form of equality. Second, the existential consequences cannot be reused, since it is not possible to deal with existential information in LP rules.

Besides the approaches outlined above, one could envision other forms of integration. (7) contains a survey of the representational issues which need to be overcome when integration ontologies based on classical logic (such as OWL DL) with rules.

(1) Francesco M. Donini, Daniele Nardi, and Riccardo Rosati. Description logics of minimal knowledge and negation as failure. ACM Transactions on Computational Logic, 3(2):177–225, April 2002.
(2) Jos de Bruijn. Ontology languages around FOL and LP. WSML Working Draft.
(3) Benjamin Grosof, Ian Horrocks, Raphael Volz, and Stefan Decker. Description logic programs: Combining logic programs with description logics. In: Proc. of WWW 2003, Budapest, Hungary, May 2003, ACM (2003) 48–57.
(4) Ulrich Hustadt, Boris Motik, Ulrike Sattler. Data complexity of reasoning in very expressive description logics. In: Proc. 19th Int. Joint Conf. on Artificial Intelligence (IJCAI). (2005) 466–471.
(5) Markus Krötzsch, Pascal Hitzler, Michael Sintek, Denny Vrandecic. Expressive OWL Reasoning with Logic Programs. Technical Report, Institute AIFB, University of Kalrsruhe. November 2005. Submitted.
(6) Thomas Eiter, Thomas Lukasiewicz, Roman Schindlauer, and Hans Tompits. Combining answer set programming with description logics for the semantic web. In Proc. of the International Conference of Knowledge Representation and Reasoning (KR04), 2004.
(7) Jos de Bruijn, Thomas Eiter, Axel Polleres, Hans Tompits: "On Representational Issues about Combinations of Classical Theories with Nonmonotonic Rules", DERI Technical Report 2006-05-29. To be published as an invited paper in the Proceedings of the First International Conference on Knowledge Science, Engineering and Management (KSEM'06), LNAI, Springer-Verlag.