SWRL (Semantic Web Rule Language) extends OWL syntax and semantics by enabling the description of Horn-like rules. However, the current SWRL specification lacks support for, among others, negative expressions, missing values and priority relationships between rules, which are frequently needed when modeling realistic scenarios. This paper motivates the necessity of surpassing some of these problems and provides an extension over the original SWRL aimed to define more expressive rules. Hence, the following four operators have been added to SWRL: Not operator (i.e., classical negation) to express negative facts; NotExists quantifier to ask for missing facts in the knowledge base (when used in the antecedent of the rule) and remove facts (when used in the consequent); Dominance operator to establish priorities among rules; and Mutex operator to establish exclusions during rule executions. The syntax and semantics of these four operators are described in this proposal. Moreover, the non-monotonicity added to the rule-based inference process by means of such elements is also explained. An implementation of the four operators has been developed as a plug-in for the Jena generic rule engine, which enables the execution of Horn-like rules, together with a parser to translate SWRL rules to the Jena specific rule language. Finally, the proposed SWRL extension and its implementation have been validated in a real scenario centered on call forwarding management in an intelligent building.