A Proposal for an
OWL Rules Language

Semantics and Abstract Syntax

Draft Version of 29 October 2003

This version:
http://www.daml.org/rules/proposal/OWL-rules-20031027/
Latest version:
http://www.daml.org/rules/proposal/
Previous version:
http://www.cs.man.ac.uk/~horrocks/DAML/Rules/WD-OWL-rules-20031016/
Authors:
Ian Horrocks, Department of Computer Science, University of Manchester
Peter F. Patel-Schneider, Bell Labs Research, Lucent Technologies
Harold Boley
Said Tabet

This document is also available as a single HTML file.


Abstract

This is a description of a proposed rules extension to the OWL Web Ontology Language. It includes a high-level abstract syntax for horn clause rules in both the OWL DL and OWL Lite sublanguages of OWL. A model-theoretic semantics is given to provide a formal meaning for OWL ontologies including rules written in this abstract syntax. An XML syntax based on the OWL XML presentation syntax and a mapping to RDF graphs based on the OWL RDF/XML exchange syntax are also given, along with several examples.

Status of this document

This is a Draft produced 29 October 2003 as part of the DARPA DAML Program.

Comments on this document are invited. Discussion should take place on www-rdf-rules@w3.org.


Table of contents


1. Introduction

This document contains a proposal for a rules extension to the OWL DL and OWL Lite sublanguages of the OWL Web Ontology Language. The proposal extends the set of OWL axioms to include horn clause rules. A high-level abstract syntax is provided that extends the OWL abstract syntax described in the OWL Semantics and Abstract Syntax document [OWL S&AS]. An extension of the OWL model-theoretic semantics is also given to provide a formal meaning for OWL ontologies including rules written in this abstract syntax.

The proposed rules are of the form of an implication between an antecedent (body) and consequent (head). The intended meaning can be read as: whenever the conditions specified in the antecedent hold, then the conditions specified in the consequent must also hold.

Both the antecedent (body) and consequent (head) consist of zero or more atoms. An empty antecedent is treated as trivially true (i.e. satisfied by every interpretation), so the consequent must also be satisfied by every interpretation; an empty consequent is treated as trivially false (i.e., not satisfied by any interpretation), so the antecedent must also not be satisfied by any interpretation. Multiple atoms are treated as a conjunction. Note that rules with conjunctive consequents could easily be transformed (via the Lloyd-Topor transformations [Lloyd87]) into multiple rules each with an atomic consequent.

Atoms in these rules can be of the form C(x), P(x,y), sameAs(x,y) or differentFrom(x,y), where C is an OWL description, P is an OWL property, and x,y are either variables, OWL individuals or OWL data values. It is easy to see that OWL DL becomes undecidable when extended in this way as rules can be used to simulate role value maps [Schmidt-Schauß89].

As well as an extension of the OWL abstract syntax, an extension of the OWL XML syntax is given for these rules, and some comments on how to provide an RDF/XML syntax for these rules.


Acknowledgments

This document has benefited from extensive discussion in the Joint US/EU ad hoc Agent Markup Language Committee. Section 6, in particular, was the result of feedback from and discussions with Benjamin Grosof and Mike Dean.


References

[OWL S&AS]
OWL Web Ontology Language Semantics and Abstract Syntax. Peter F. Patel-Schneider, Pat Hayes and Ian Horrocks, eds.
[OWL Reference]
OWL Web Ontology Language 1.0 Reference. Mike Dean, Dan Connolly, Frank van Harmelen, James Hendler, Ian Horrocks, Deborah L. McGuinness, Peter F. Patel-Schneider, and Lynn Andrea Stein. W3C Working Draft 12 November 2002. Latest version is available at http://www.w3.org/TR/owl-ref/.
[OWL XML]
OWL Web Ontology Language XML Presentation Syntax. Masahiro Hori, Jérôme Euzenat, Peter F. Patel-Schneider. W3C Note 11 June 2003
[Lloyd87]
Foundations of logic programming (second, extended edition). J. W. Lloyd. Springer series in symbolic computation. Springer-Verlag, New York, 1987.
[Schmidt-Schauß89]
Subsumption in KL-ONE is Undecidable. M. Schmidt-Schauß. Proc. of KR'89, pages 421-431, Morgan Kaufmann.
[Grosof et al 2003]
Description Logic Programs: Combining Logic Programs with Description Logic. Benjamin Grosof, Ian Horrocks, Raphael Volz, Stefan Decker. Proc. WWW2003, Budapest, May 2003. http://www2003.org/cdrom/papers/refereed/p117/p117-grosof.html (also http://ebusiness.mit.edu/bgrosof/#DLP).
[RuleML]
Rule Markup Language Initiative.