We investigate a logical semantics which unambiguously specifies the meaning of SQL-like referential actions of the form ON DELETE CASCADE and ON DELETE RESTRICT. The semantics is given by a translation of referential actions into logical rules. The proposed semantics is less restrictive than the standard SQL semantics, yet preserves all referential integrity constraints. First, a preliminary set of rules is introduced which rejects a set of user requests if a single request is rejected. Subsequently, a refined translation is presented using Statelog, a state-oriented Datalog extension which allows to define active and deductive rules within a unified framework. We show that our semantics yields the maximal admissible subset of a given set of user requests. Apart from the Statelog formalization, a three-valued formalization based on the well-founded semantics and an equivalent game-theoretic specification are presented, which give further insight into the problem of ambiguity of triggers.

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Followup papers have been published in PODS 1997 and TODS 27(4), 2002.
An extended version containing these results can be found in Understanding the Global Semantics of Referential Actions using Logic Rules, Wolfgang May, Bertram Ludäscher, ACM Transactions on Database Systems (TODS), 27(4), 2002.