Linear tabulated resolution based on Prolog control strategy

Abstract

Infinite loops and redundant computations are long recognized open problems in Prolog. Two ways have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for function-free logic programs. Tabling seems to be an effective way to resolve infinite loops and redundant computations. However, existing tabulated resolutions, such as OLDT-resolution, SLG-resolution, and Tabulated SLS-resolution, are non-linear because they rely on the solution-lookup mode in formulating tabling. The principal disadvantage of non-linear resolutions is that they cannot be implemented using a simple stack-based memory structure like that in Prolog. Moreover, some strictly sequential operators such as cuts may not be handled as easily as in Prolog.In this paper, we propose a hybrid method to resolve infinite loops and redundant computations. We combine the ideas of loop checking and tabling to establish a linear tabulated resolution called TP-resolution. TP-resolution has two distinctive features: (1) It makes linear tabulated derivations in the same way as Prolog except that infinite loops are broken and redundant computations are reduced. It handles cuts as effectively as Prolog. (2) It is sound and complete for positive logic programs with the bounded-term-size property. The underlying algorithm can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.

GEM: A distributed goal evaluation algorithm for trust management

“…The most commonly employed technique to prevent infinite derivations is tabling (Bry 1989;Chen and Warren 1996;Guo and Gupta 2001;Shen et al 2001;Tamaki and Sato 1986;Vieille 1987;Zhou and Sato 2003). Given a goal G 0 consisting of an atom defined in a program P , tabling-based goal evaluation algorithms create a table for each (sub)goal in the SLD resolution of P ∪ {G 0 }, to keep track of the previously evaluated goals and thus avoid the reevaluation of a subgoal.…”

“…SLG resolution (Chen and Warren 1996), TP-resolution (Shen et al 2001), DRA (Guo and Gupta 2001), OPTYap (Rocha et al 2005), and the work by Hulin (1989) are centralized tabling systems in which the complete program (i.e., the global policy) is available during the evaluation. Therefore, these five systems are classified as E1-I3 according to the classification criteria defined in Section 3.1, that is, they do not preserve the confidentiality of neither extensional nor intensional policies.…”

“…OPTYap resorts to centralized data structures to identify loops and detect termination. In (Hulin 1989) (Chen and Warren 1996) centralized centralized centralized E1-I3 TP resolution (Shen et al 2001) centralized centralized centralized E1-I3 DRA (Guo and Gupta 2001) centralized centralized centralized E1-I3 OPTYap (Rocha et al 2005) centralized centralized centralized E1-I3 Hulin (1989) centralized centralized centralized…”

Modal logic programming revisited

“…There are advanced tabulation methods for Prolog like OLDT-resolution (Tamaki et al, 1986), linear tabulated resolution (Shen et al, 2001;Zhou et al, 2003). These methods use sophisticated techniques (e.g.…”

A Generalized QSQR Evaluation Method for Horn Knowledge Bases

“…Tabled SLD-resolution systems like OLDT [Tamaki and Sato 1986], SLD-AL [Vieille 1987;1989], linear tabulated resolution [Shen et al 2001;Zhou and Sato 2003] are efficient computational procedures for logic programming without redundant recomputations, but they are not directly applicable to Horn knowledge bases to obtain efficient evaluation engines because they are not set-oriented (set-at-a-time). In particular, the suspension-resumption mechanism and the stack-wise representation as well as the "global optimizations of SLD-AL" are all tuple-oriented (tuple-at-a-time).…”