Minimal Semantics for Transaction Speci cations in aMulti - modal

This paper presents an extension of propositional dynamic database logic in which arbitrary database transactions can be speciied declaratively. Typically, declaratively speciied transactions are under-speciied. Speciications are usually supplemented with a frame assumption about what does not change as the result of a transaction, and a qualiication assumption stating that transactions occur, provided they respect certain conditions called 'guards' and do not contravene any constraints. In addition these (static) constraints may be, or may not be interpreted to force ramiications of transactions. In the former case, both frame and qualiication assumption should also apply to ramiications. We solve these problems by deening preferences over Kripke structures and showing how these can be used to deene an intended semantics that, for each declarative transaction speciication, selects a unique meaning for each transaction. In particular, the intended semantics formalizes a frame assumption and selects qualiications and ramiications for each speciication. The notion of preferential entailment based on the semantics provides a natural way of reasoning about declaratively speciied transactions.