Techniques for Efficient Lazy-Grounding ASP Solving

46 Pages·2017·0.2 MB·English

Techniques for Efficient
Lazy-Grounding ASP Solving
LorenzLeutgeb1 AntoniusWeinzierl1,2
September19,2017
1Knowledge-BasedSystemsGroup
TUWien,Vienna,Austria
2DepartmentofComputerScience
AaltoUniversity,Helsinki,Finland
Introduction
Motivation
• Answer-SetProgramming(ASP):well-establishedKRformalism.
• Rule-based,nonmonotonic,expressive.
• TraditionalASPsolvingtwo-phased: groundandsolve.
• Problem: groundingofexponentialsizeingeneralandpractice.
⇒ GroundingbottleneckofASP.
Example
dom(1). dom(2). ... dom(20).
sel(X) ← dom(X),notnsel(X).
nsel(X) ← dom(X),notsel(X).
← sel(Y),sel(X),X! = Y.
p(X ,X ,X ,X ,X ,X ) ← sel(X ),sel(X ),sel(X ),
1 2 3 4 5 6 1 2 3
sel(X ),sel(X ),sel(X ).
4 5 6
1
Motivation
• Answer-SetProgramming(ASP):well-establishedKRformalism.
• Rule-based,nonmonotonic,expressive.
• TraditionalASPsolvingtwo-phased: groundandsolve.
• Problem: groundingofexponentialsizeingeneralandpractice.
⇒ GroundingbottleneckofASP.
Example
dom(1). dom(2). ... dom(20).
sel(X) ← dom(X),notnsel(X).
nsel(X) ← dom(X),notsel(X).
← sel(Y),sel(X),X! = Y.
p(X ,X ,X ,X ,X ,X ) ← sel(X ),sel(X ),sel(X ),
1 2 3 4 5 6 1 2 3
sel(X ),sel(X ),sel(X ).
4 5 6
1
Lazy-Grounding ASP Solving
• Lazy-Grounding: interleavegroundingandsolving
⇒Avoidgroundingbottleneck.
• Basedoncomputationsequences.
• Existingsolvers: Gasp,AsPeRiX,Omiga.
• Nostrongsearchspacereducingtechniques
(likeconflict-drivenlearning,backjumping,heuristics,etc).
• Groundingstrongly-coupledtosearch(grounderbacktracks).
⇒ Badsearchperformance.
2
The Alpha Solver
• Novelapproachatlazy-grounding(firstpresentedatLPNMR’17).
• Twocomponents: lazy-grounderandmodifiedCDNLsolver.
• Blendlazy-groundingandstate-of-the-artCDNL-basedsearch.
• Representrulesbynogoods(similartoClasp/Clingo).
• Loose-couplingoflazy-groundingandsearch.
• Goal: Lazy-groundingwithgoodsearchperfomance.
3
Overview of Alpha
Architecture of Alpha
Nogoods
Grounder Solver
Program Conflict Nogood
Parser
Resolution Storage
Lazy- Choice Decision
Assignment
Grounding Atoms Heuristic
Answer-Set
partialAssignment
Figure1: Alphaarchitecture,arrowsindicatedataflow.
4
Representing Rules
• Constraint: ← sel(1),sel(2).
• Nogood: ng = {Tsel(1),Tsel(2)}.
• Problem: distinguish← nota,b.froma ← b.
• State-of-the-artsolution,addconstraintexpressing:
“Ifaistrue,theremustbearulefiringwithainitshead.”
• Lazy-groundingcannotknowallruleswithainthehead:
a ← p(X).
• SolutioninAlpha:
• Nogoodsmayhaveheadandthirdtruthvaluemust-be-true.
• Propagate: totrueifheadofnogoodisimplied,otherwiseto
must-be-true(andfalse).
• Nogood{Fa,Tb}distinctfrom{Fa,Tb} withhead.
1
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Representing Rules
• Constraint: ← sel(1),sel(2).
• Nogood: ng = {Tsel(1),Tsel(2)}.
• Problem: distinguish← nota,b.froma ← b.
• State-of-the-artsolution,addconstraintexpressing:
“Ifaistrue,theremustbearulefiringwithainitshead.”
• Lazy-groundingcannotknowallruleswithainthehead:
a ← p(X).
• SolutioninAlpha:
• Nogoodsmayhaveheadandthirdtruthvaluemust-be-true.
• Propagate: totrueifheadofnogoodisimplied,otherwiseto
must-be-true(andfalse).
• Nogood{Fa,Tb}distinctfrom{Fa,Tb} withhead.
1
5