Extending OCL with Null-References: Towards a Formal Semantics for OCL 2.1

From its beginnings, OCL is based on a strict semantics for undefinedness, with the exception of the logical connectives of type Boolean that constitute a three-valued propositional logic. Recent versions of the OCL standard added a second exception element, which, similar to the null references in object-oriented programming languages, is given a non-strict semantics. Unfortunately, this extension has been done in an ad hoc manner, which results in several inconsistencies and contradictions. In this paper, we present a consistent formal semantics (based on our HOL-OCL approach) that includes such a non-strict exception element. We discuss the possible consequences concerning class diagram semantics as well as deduction rules. The benefits of our approach for the specification-pragmatics of design level operation contracts are demonstrated with a small case-study.