A New Formulation of Tabled Resolution with Delay

Tabling has become important to logic programming in part because it opens new application areas, such as model checking, to logic programming techniques. However, the development of new extensions of tabled logic programming is becoming restricted by the formalisms that underly it. Formalisms for tabled evaluations, such as SLG [3], are generally developed with a view to a specific set of allowable operations that can be performed in an evaluation. In the case of SLG, tabling operations are based on a variance relation between atoms. While the set of SLG tabling operations has proven useful for a number of applications, other types of operations, such as those based on a subsumption relation between atoms, can have practical uses. In this paper, SLG is reformulated in two ways: so that it can be parameterized using different sets of operations; and so that a forest of trees paradigm is used. Equivalence to SLG of the new formulation, Extended SLG or SLGX, is shown when the new formalism is parameterized by variant-based operations. In addition, SLGX is also parameterized by subsumption-based operations and shown correct for queries to the well-founded model. Finally, the usefulness of the forest of trees paradigm for motivating tabling optimizations is shown by formalizing the concept of relevance within a tabled evaluation.