In this paper we proposed a new semantics for the combination of production systems with
ontologies. Unlike previous approaches, the semantics presented here allow looping rules and can handle inconsistencies produced by the interaction of the rule actions and the ontology. We also define a sound embedding of such semantics, restricted to rule-based
Ontologies, into Transaction Logic with partial action definitions (
). This reduction adds a declarative semantics to the combination. To model production systems in
, we extend
with default negation and define the well-founded semantics for it.