Minimal Semantics for Transaction Speciications in a Multi-modal Logic

This paper presents an extension of propositional dynamic database logic in which the speciication writer can specify arbitrary database transactions declaratively. Since declaratively speciied transactions are under-speciied, the speciication must be supplemented with a frame assumption about what does not change as the result of a transaction. In addition , static database constraints imply preconditions, also called qualiications , that must be satissed for a transaction to occur and static constraints may imply derived updates for a transaction (also called 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.