A complete logic for Database Abstract State Machines1

In database theory, the term database transformation was used to refer to a unifying treatment for computable queries and updates. Recently, it was shown that non-deterministic database transformations can be captured exactly by a variant of ASMs, the so-called Database Abstract State Machines (DB-ASMs). In this article we present a logic for DBASMs, extending the logic of Nanchen and Stärk for ASMs. In particular, we develop a rigorous proof system for the logic for DB-ASMs, which is proven to be sound and complete. The most difficult challenge to be handled by the extension is a proper formalisation capturing non-determinism of database transformations and all its related features such as consistency, update sets or multisets associated with DB-ASM rules. As the database part of a state of database transformations is a finite structure and DB-ASMs are restricted by allowing quantifiers only over the database part of a state, we resolve this problem by taking update sets explicitly into the logic, i.e. by using an additional modal operator [X], where X is interpreted as an update set ∆ generated by a DB-ASM rule. The DB-ASM logic provides a powerful verification tool to study properties of database transformations. Acknowledgements. The research reported in this paper results from the project Behavioural Theory and Logics for Distributed Adaptive Systems supported by the Austrian Science Fund (FWF): [P26452-N15]. It was further supported by the Austrian Research Promotion Agency (FFG) through the COMET funding for the Software Competence Center Hagenberg.