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Tabling with Sound Answer Subsumption

Published online by Cambridge University Press:  14 October 2016

ALEXANDER VANDENBROUCKE ,
MACIEJ PIRÓG ,
BENOIT DESOUTER  and
TOM SCHRIJVERS
ALEXANDER VANDENBROUCKE
Affiliation:
KU Leuven, Belgium (e-mail: alexander.vandenbroucke@kuleuven.be)
MACIEJ PIRÓG
Affiliation:
KU Leuven, Belgium (e-mail: maciej.pirog@kuleuven.be)
BENOIT DESOUTER
Affiliation:
Ghent University, Belgium (e-mail: benoit.desouter@ugent.be)
TOM SCHRIJVERS
Affiliation:
KU Leuven, Belgium (e-mail: tom.schrijvers@kuleuven.be)
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Abstract

Tabling is a powerful resolution mechanism for logic programs that captures their least fixed point semantics more faithfully than plain Prolog. In many tabling applications, we are not interested in the set of all answers to a goal, but only require an aggregation of those answers. Several works have studied efficient techniques, such as lattice-based answer subsumption and mode-directed tabling, to do so for various forms of aggregation.

While much attention has been paid to expressivity and efficient implementation of the different approaches, soundness has not been considered. This paper shows that the different implementations indeed fail to produce least fixed points for some programs. As a remedy, we provide a formal framework that generalises the existing approaches and we establish a soundness criterion that explains for which programs the approach is sound.

Keywords

tablinganswer subsumptionlatticepartial ordermode-directed tablingdenotational semanticsProlog
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 16 , Special Issue 5-6: 32nd International Conference on Logic Programming , September 2016 , pp. 933 - 949
Copyright
Copyright © Cambridge University Press 2016 

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