Tabled logic programming: Difference between revisions

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Tabling is a technique first developed for natural language processing, where it was called [[Earley parsing]] (Kay Reference Kay1967; Earley Reference Earley1970). It consists of storing in a table (a.k.a. chart in the context of parsing) partial successful analyses that might come in handy for future reuse.

Its adaptation into a logic programming proof procedure, under the name of Earley deduction, dates from an unpublished note from 1975 by David H.D. Warren, as documented by Pereira and Shieber (Reference Pereira and Shieber1987). An interpretation method based on tabling was later developed by Tamaki and Sato (Reference Tamaki and Sato1986), modeled as a refinement of SLD-resolution.

David S. Warren ^Footnote5 and his students adopted this technique with the motivation of changing Prolog’s semantics from the completion semantics to the minimal model semantics.

Indeed, the completion semantics cannot faithfully capture important concepts such as the transitive closure of a graph or relation. The minimal model semantics is able to capture such concepts. Moreover, tabled execution terminates for corresponding programs such as for the transitive closure of a cyclic graph. This makes Prolog more declarative.

Tabling consists of maintaining a table of goals that are called during execution, along with their answers, and then using the answers directly when the same goal is subsequently called. Tabling gives a guarantee of total correctness for any (pure) Prolog program without function symbols, which was one of the goals of that work.

== History ==

''XSB Prolog (1994)'' The concept of tabled Prolog was introduced in XSB Prolog (Sagonas ''et al.'' Reference Sagonas, Swift and Warren1994). This resulted in a complete implementation (Rao ''et al.'' Reference Rao, Sagonas, Swift, Warren, Freire and Notes1997) of the [[well-founded semantics]] (Van Gelder ''et al.'' Reference Van Gelder, Ross and Schlipf1991), a three-valued semantics that represents values for true, false and unknown.

ItsThe adaptation of tabling into a logic programming proof procedure, under the name of Earley deduction, dates from an unpublished note from 1975 by David H.D. Warren, as documented by Pereira and Shieber (Reference Pereira and Shieber1987). An interpretation method based on tabling was later developed by Tamaki and Sato (Reference Tamaki and Sato1986), modeledmodelled as a refinement of SLD-resolution.

David S. Warren ^Footnote5 and his students adopted this technique with the motivation of changing Prolog’s semantics from the completion semantics to the minimal model semantics.

''XSB Prolog (1994)'' The concept of tabled Prolog was introduced in [[XSB|XSB Prolog]] (Sagonas ''et al.'' Reference Sagonas, Swift and Warren1994). This resulted in a complete implementation (Rao ''et al.'' Reference Rao, Sagonas, Swift, Warren, Freire and Notes1997) of the [[well-founded semantics]] (Van Gelder ''et al.'' Reference Van Gelder, Ross and Schlipf1991), a three-valued semantics that represents values for true, false and unknown.

== References ==