Concurrency and Communication in Transaction Logic

In previous work, we developed Transaction Logic (or TR), which deals with state changes in deductive databases. TR provides a logical framework in which elementary database updates and queries can be combined into complex database transactions. TR accounts not only for the updates themselves, but also for important related problems, such as the order of update operations, non-determinism, and transaction failure and rollback. In the present paper, we propose Concurrent Transaction Logic (or CTR), which extends Transaction Logic with connectives for modeling the concurrent execution of complex processes. Concurrent processes in CTR execute in on interleaved fashion and can communicate and synchronize themselves. Like classical logic, CTR has a “Horn” fragment that has both a procedural and a declarative semantics, in which users can program and execute database transactions. CTR is thus a deductive database language that integrates concurrency, communication, and updates. All this is accomplished in a completely logical framework, including a natural model theory and a proof theory. Moreover, this framework is flexible enough to accommodate many different semantics for updates and deductive databases. For instance, not only can updates insert and delete tuples, they can also insert and delete null values, rules, or arbitrary logical formulas. Likewise, not only can databases have a classical semantics, they can also have the well-founded semantics, the stable-model semantics, etc. Finally, the proof theory for CTR has an efficient SLD-style proof procedure. As in the sequential version of the logic, this proof procedure not only finds proofs, it also executes concurrent transactions, finds their execution schedules, and updates the database. A main result is that the proof theory is sound and complete for the model theory.