Denotational Semantics of Object Specification Within an Arbitrary Temporal Logic Institution

From an arbitrary temporal logic institution we show how to set-up the corresponding institution of objects. The main properties of the resulting institution are studied and used in establishing the denotational, categorial semantics of several basic object specification constructs, namely aggregation (parallel composition), interconnection, abstraction (interfacing) and monotonic specialization. An isomorphism is established between the category of theories and the category of objects, as a corollary of the Galois correspondence between these concrete categories. The special case of linear temporal logic is analysed in detail in order to show that categorial products do reflect interleaving, and reducts may lead to internal non-determinism.