Using Relaxation Techniques to Evaluate Queries in Deductive Databases

Relaxation method is a general framework used to improve the efficiency of answering a query q(a, x) given to a deductive database P. It first solves problem (q'(a', x'), P^), where P^ is a relaxation of the original database P and q'(a', x') is the modified query to P^, to derive a set PREL of predicate occurrences that is known to contain the answer set ANS in P, and construct database P^ by augmenting P with the restriction that solution space is constrained to PREL, and finally solves problem (q(a, x), P^) to get the desired answer set ANS. If the relaxation P^ is properly defined, (q'(a', x'), P^) can be efficiently solved since P^ is simpler than P, and (q(a, x), P^) can also be efficiently solved as the solution space is restricted. Several methods are proposed to construct such relaxations. It is also argued that the original form of magic set method [2] can be described in the context of the relaxation method