Integrity constraint checking in stratified databases

The above method is a refinement of the LST method in that Θ is used not only to simplify integrity constraints at the topmost level but throughout testing to prune non-relevant branches.

“The above method can be seen as a refinement of the LST method [61], in the sense that Θ is not only used to simplify the integrity constraints at the topmost level (i.e. affecting the bodies of integrity constraints), but is used throughout the testing of the integrity constraints to prune non-relevant branches.”

The main difference with the exposition in [63,61] is that the authors calculate pos(U) and neg(U) in one step instead of in two.

“The main difference with the exposition in [63,61] is that we calculate pos(U) and neg(U) in one step instead of in two.”

The LST method not only removes integrity constraints but also instantiates them, possibly generating several specialised integrity constraints for a single unspecialised one.

“However, the LST method [61] not only removes integrity constraints but also instantiates them, possibly generating several specialised integrity constraints for a single unspecialised one.”

For the example database with Db+ = {man(a) ←}, Db− = ∅, the LST method of [61] generates the simplified integrity constraints false ← man(a), woman(a) and false ← parent(a, Y), unmarried(a), independently of the facts in Db=.

“The LST method of [61] will then generate the following simplified integrity constraints:”

The LST techniques [61] often perform very well in practice, even for relational or hierarchical databases [22].

“compare their efficiency with the one of the LST techniques [61], which often performs very well in practice, even for relational or hierarchical databases [22].”

Running LST on a generic update allowed the deduction that the second integrity constraint cannot be violated by the update, while the other integrity constraints remain unchanged.

“So, by running LST on a generic update we were just able to deduce that the second integrity constraint cannot be violated by the update – the other integrity constraints remain unchanged.”

Some existing integrity checking methods, such as the Lloyd-Sonenberg-Topor method [61], are not amenable to specialisation using current techniques.

“We have also argued why some existing integrity checking methods, like, e.g., the Lloyd-Sonenberg-Topor method [61], are not amenable to specialisation using current techniques.”

Even for relational databases with complex views, deductive database approaches such as the LST method [61] seem to be the most competitive ones available.

“However, even for relational databases - with complex views – the deductive database approaches, such as the LST method [61], seem to be the most competitive ones available.”

Compared with an unspecialised implementation of the well known approach by Lloyd et al. [61], the results show that big performance improvements, also reaching and exceeding 2 orders of magnitude, can be obtained.

“We also compared the specialised update procedures with an unspecialised implementation of the well known approach by Lloyd et al. in [61], and the results show that big performance improvements, also reaching and exceeding 2 orders of magnitude, can be obtained.”