**
Understanding the Global Semantics of Referential Actions using
Logic Rules
**

Wolfgang May , Bertram Ludäscher

**Abstract:**

Referential actions are specialized triggers for automatically
maintaining referential integrity in databases. While the
*local effects* of referential actions can be grasped easily,
it is far from obvious what the *global semantics* of a set of
interacting referential actions should be. In particular, when
using procedural execution models, ambiguities due to the execution
ordering can occur. No *global, declarative* semantics of
referential actions has been defined yet.

We show that the well-known logic programming semantics provide a
natural *global* semantics of referential actions that is
based on their *local* characterization: To capture the
global meaning of a set *RA* of referential actions, we first
define their abstract (but non-constructive) *intended
semantics*. Next, we *formalize* *RA* as a
*logic program* *P _{RA}*. The declarative, logic
programming semantics of

We first focus on the subset of referential actions for deletions
only. We prove the equivalence of the logic programming
semantics and the abstract semantics via a game-theoretic
characterization, which provides additional insight into the meaning
of interacting referential actions. In this case a
*unique maximal admissible solution exists*, computable by a
PTIME algorithm.

Second, we investigate the general case, i.e. including
modifications. We show that in this case there can be *multiple
maximal admissible subsets* and that all maximal admissible
subsets can be characterized as *3-valued stable models* of
*P _{RA}*. We show that for a given set of user
requests, in presence of referential actions of the form