Proof-Theoretic Semantics of Object-Oriented Specification Constructs

A formal semantics for the kernel constructs of an object-oriented specification language is presented. The formal counterparts of objects as the basic building blocks of information systems are given by theory presentations in a logic that has been developed to support the required object-oriented specification mechanisms. Attributes (structure) and events (behaviour) are integrated in coherent logical units (focused on a logical rôle for signatures) around which the notion of locality (encapsulation) is formalised. Objects can be specified directly through formulae of the logic, describing the effects of the events on the attributes as well as the restrictions and requirements on their occurrence. Aggregation, inheritance and particularisation are formalised as specification constructs acting on a context (a diagram in the category of theory presentations) where previously built specifications are stored, thus allowing to assemble large specifications from existing ones. The derivation of safety and liveness properties from specifications using the inference rules of the logic, and the use of the structure of specifications to direct these proofs is also illustrated. In this way, we hope to contribute towards the necessary formalisation of object-oriented information systems design.