Combining Production Systems and Ontologies Mart´ ın Rezk and Werner Nutt KRDB Research Centre, Faculty of Computer Science Free University of Bozen-Bolzano, Italy {rezk,nutt}@inf.unibz.it Abstract. Production systems are an established paradigm in knowledge repre- sentation, while ontologies are widely used to model and reason about the domain of an application. Description logics, underlying for instance the Web ontology language OWL, are a well-studied formalism to express ontologies. In this work we combine production systems (PS) and Description Logics (DL) in such a way that allows one to express both, facts and rules, using an ontology language. We explore the space of design options for combining the traditional closed world semantics of PS with the open world semantics of DL and propose a generic semantics for such combination. We show how to encode our semantics in a fix- point extension of first-order logic. We show that in special cases (monotonic and light PS) checking properties of the system such as termination is decidable. 1 Introduction Production systems (PS) are one of the oldest knowledge representation paradigms in Artificial Intelligence, and are still widely used today. We consider PSs that consist of (i) a set of rules r of the form if φ r then ψ r (1) (ii) a set of ground facts, called working memory, which contains the current state of knowledge, and (iii) a rule interpreter, which executes the rules and makes changes in the working memory, based on the actions in the rules. The condition φ r is a FOL for- mula, and the action ψ r =+a 1 ,..., +a k , ∼b 1 ,..., ∼b l where each +a i and ∼b j stand for asserting and retracting an atomic fact (atom) to/from the working memory. These rules syntactically correspond to the fragment of the RIF Production Rule Dialect 1 that does not include the forall construct, modify actions, external functions, etc. Semanti- cally it deviates from RIF on the fact that we assume that all the actions are applied simultaneously. Given a working memory, the rule interpreter applies the rules in three steps: (1) pattern matching—typically using the RETE algorithm [5]—(2) conflict res- olution–the interpreter chooses zero or one pair among the rules whose condition is satisfied according to its strategy—and (3) rule execution. The formal semantics for a PS can be found in [3]. PSs do not provide a way to express knowledge about the domain, and the relations among terms in the PS vocabulary. Moreover, they cannot handle incomplete informa- tion. Description Logic (DL) ontologies [1] are a standard way to achieve that. In this work we consider standard DLs without nominals. For concreteness, we will work with 1 http://www.w3.org/TR/rif-prd/ S. Rudolph and C. Gutierrez (Eds.): RR 2011, LNCS 6902, pp. 287–293, 2011. c  Springer-Verlag Berlin Heidelberg 2011