Foundations of Behavioural Specification in Rewriting Logic

We extend behavioural specification based on hidden sorts to rewriting logic by constructing a hybrid between the two underlying logics. This is achieved by defining a concept of behavioural satisfaction for rewriting logic. Our approach is semantic in that it is based on a general construction on models, called behaviour image, which uses final models in an essential way. However we provide syntactic characterisations for the for the behavioural satisfaction relation, thus opening the door for shifting recent advanced proof techniques for behavioural satisfaction to rewriting logic. We also show that the rewriting logic behavioural satisfaction obeys the socalled "satisfaction condition" of the theory of institutions, thus providing support for OBJ style modularisation for this new paradigm. 1 Introduction This research aims at integrating two different semantic approaches on objects and concurrency by internalising behavioural specification [12] to [conditional] rewriting logic (abb..