Formal Semantics of Dynamic Rules in ORM

This paper provides formal semantics for an extension of the ObjectRole Modeling approach that supports declaration of dynamic rules. Dynamic rules differ from static rules by pertaining to properties of state transitions, rather than to the states themselves. In this paper we restrict application of dynamic rules to so-called single-step transactions, with an old state (the input of the transaction) and a new state (the direct result of that transaction). These dynamic rules further specify an elementary transaction type by indicating which kind of object or fact (being added, deleted or updated) is actually allowed. Dynamic rules may declare pre-conditions relevant to the transaction, and a condition stating the properties of the new state, including the relation between the new state and the old state. In this paper we provide such dynamic rules with a formal semantics based on sorted, first-order predicate logic. The key idea to our solution is the formalization of dynamic constraints as static constraints on the database transaction history.