Terminating Evaluation of Logic Programs with Finite Three-Valued Models

As evaluation methods for logic programs have become more sophisticated, the classes of programs for which termination can be guaranteed have expanded. From the perspective of ar set programs that include function symbols, recent work has identified classes for which grounding routines can terminate either on the entire program [Calimeri et al. 2008] or on suitable queries [Baselice et al. 2009]. From the perspective of tabling, it has long been known that a tabling technique called subgoal abstraction provides good termination properties for definite programs [Tamaki and Sato 1986], and this result was recently extended to stratified programs via the class of bounded term-size programs [Riguzzi and Swift 2013]. In this article, we provide a formal definition of tabling with subgoal abstraction resulting in the SLGSA algorithm. Moreover, we discuss a declarative characterization of the queries and programs for which SLGSA terminates. We call this class strongly bounded term-size programs and show its equivalence to programs with finite well-founded models. For normal programs, strongly bounded term-size programs strictly includes the finitely ground programs of Calimeri et al. [2008]. SLGSA has an asymptotic complexity on strongly bounded term-size programs equal to the best known and produces a residual program that can be sent to an answer set programming system. Finally, we describe the implementation of subgoal abstraction within the SLG-WAM of XSB and provide performance results.