Finite representation of infinite query answers

Abstract

and TOMASZ IMIELINSKI Rutgers UniversityWe define here a formal notion of finite representation of infinite query answers in logic programs. We apply this notion to Datalog.s (Datalog with n successors): an extension of Datalog capable of representing infinite phenomena like flow of time or plan construction. Predicates in Datalogns can have arbitrary unary and limited n-ary function symbols m one fixed position. This class of logic programs is known to be decidable.However, least Herbrand modek of Data log.~programs may be infinite and consequently queries may have infinite answers.We present a method to finitely represent infinite least Herbrand models of Datalog.s programs as relational specifications. A relational specificationconsistsof a finite set of facts and a finitely specified congruencerelation. A relational specification has the following desirable properties: First, it is explicit in the sense that once it is computed, the original Datalog,zs program (and its underlying computational engine) can be forgotten. Given a query to be evaluated, it is easy to obtain from the relational specification finitely many answer substitutions that represent infinitely many answer substitutions to the query. The method involved is a combination of a simple, unificationless, computational mechanism(graph traversal, congruence closure, or term rewriting) and standard relational query evaluation methods. Second,a relationa I specificationis effectively computable and its computation is no harder, in the senseof the comp~exityclass,than answering yes-noqueries.Our method is applicable to every range-restricted Datalogns program. We also showthat for somevery simple non-Datalogn~logic programs, finite representations of query answers do not exist.

On Reasoning about Structural Equality in XML: A Description Logic Approach

“…This approach has several advantages. First, the decidability and complexity of logical implication for DLFD reg is closely related to reasoning in Datalog ∨,¬ nS , a logic programming language of monadic predicates and functions [12,13]. Second, the use of Datalog ∨,¬ nS provides a uniform framework in which we can study various extensions of DLFD reg , how roles can be simulated by attributes for example.…”

“…It is known that a Datalog ∨,¬ nS program has a model if and only if it has a Herbrand model [12,13,27]; this allows the use of syntactic techniques for model construction. To establish the complexity bounds we use the following result for the satisfiability of Datalog ∨,¬ nS programs [13,18].…”

“…To establish the complexity bounds we use the following result for the satisfiability of Datalog ∨,¬ nS programs [13,18]. …”

Symbolic user-defined periodicity in temporal relational databases

“…Thus, in general, the definition of [ P (and of P and À P ) involve considering the fragments (e.g., [10,12), [12,13), [13,13], (13,15], [16,16], [19,20] in the example above) of frame times of the tuples with equal data part.…”

“…Regarding the approaches based on deductive rules, consider, e.g., [15], [16], which dealt with periodicity via the introduction of the successor function in Datalog. Kabanza et al proposed a very influential approach using constraints [22], [23], that extended classical relational databases to deal with periodic data by representing infinite temporal information by generalized tuples defined by linear repeating points (points of the form c1+c2*X) and constraints on points (e.g., X1…”