Tabled evaluation with delaying for general logic programs

Abstract

SLD resolution with negation as finite failure (SLDNF) reflects the procedural interpretation of predicate calculus as a programming language and forms the computational basis for Prolog systems. Despite its advantages for stack-based memory management, SLDNF is often not appropriate for query evaluation for three reasons: (a) it may not terminate due to infinite positive recursion; (b) it may be terminate due to infinite recursion through negation; and (c) it may repeatedly evaluate the same literal in a rule body, leading to unacceptable performance. We address all three problems for goal-oriented query evaluation of general logic programs by presenting tabled evaluation with delaying, called SLG resolution. It has three distinctive features: (i) SLG resolution is a partial deduction procedure, consisting of seven fundamental transformations. A query is transformed step by step into a set of answers. The use of transformations separates logical issues of query evaluation from procedural ones. SLG allows an arbitrary computation rule for selecting a literal from a rule body and an arbitrary control strategy for selecting transformations to apply. (ii) SLG resolution is sound and search space complete with respect to the well-founded partial model for all non-floundering queries, and preserves all three-valued stable models. To evaluate a query under differenc three-valued stable models, SLG resolution can be enhanced by further processing of the answers of subgoals relevant to a query. (iii) SLG resolution avoids both positive and negative loops and always terminates for programs with the bounded-term-size property. It has a polynomial time data complexity for well-founded negation of function-free programs. Through a delaying mechanism for handling ground negative literals involved in loops, SLG resolution avoids the repetition of any of its derivation steps. Restricted forms of SLG resolution are identified for definite, locally stratified, and modularly stratified programs, shedding light on the role each transformation plays.

Key Constraints and Monotonic Aggregates in Deductive Databases

“…Memoing techniques could be used for this purpose, and for an efficient implementation of keys and aggregates [3].…”

A Tabling Implementation Based on Variables with Multiple Bindings

“…Execution fails then and backtracks over the last choice point (2). Since the trail pointer is equal to the value of the trail stored at the top of the MVBstateStack, an MVB variable is created and associated with the range from the sid of the topmost element of MVBstateStack to the last sid variable, which is 1 (Figure 6 (3)).…”

“…Tabling [1][2][3] is a strategy for executing logic programs which memoizes already processed calls and their answers to improve several of the limitations of the SLD resolution strategy. It guarantees termination for programs with the bounded term size property, improves efficiency in programs which repeatedly perform some computation, and has been successfully applied to deductive databases [4], program analysis [5,6], semantic Web reasoning [7], model checking [8], etc.…”

Uncertainty Management in Logic Programming: Simple and Effective Top-Down Query Answering

“…The attentive reader will notice that the Solve procedure is related to the so-called tabulation procedures, like [2,4]. Indeed, it is a generalization of it to arbitrary monotone equational systems over lattices.…”