PROJECTOR: an automatic logic program rewriting tool for better performance Nick Hippen & Yuliya Lierler Nick Hippen University of Nebraska at Omaha
What is Answer Set Programming (ASP)? β’ Constraint programming paradigm geared towards solving difficult combinatorial search problems β’ Prolog-like syntax Logic Rule Meaning πβπππ π, π β πππ πππ’ π, π . X is a child of Y if Y is a parent of X. ππππππππ’ π β πππ’ ππ£πππ’π§ π . X is innocent if I have no reason to believe that X is guilty Head β Body Nick Hippen University of Nebraska at Omaha 2
ASP Solver Architecture logic grounded answer Grounder ASP Solver program program sets logic rewritten logic grounded answer Grounder ASP Solver PROJECTOR program program program sets Nick Hippen University of Nebraska at Omaha 3
Grounding Logic Programs Logic Program Grounded Program Intelligently Grounded Program πππ πππ’ πππ, ππππ§ . πππ πππ’ πππ, ππππ§ . πππ πππ’ πππ, ππππ§ . πππ πππ’ πππ π π§, ππβπ . πππ πππ’ πππ π π§, ππβπ . πππ πππ’ πππ π π§, ππβπ . π‘ππππππ πππ, πππ π π§ . π‘ππππππ πππ, πππ π π§ . π‘ππππππ πππ, πππ π π§ . πππ£π‘ππ π, π β πππ πππ’ π1, π , πππ£π‘ππ ππβπ, πππ π π§ β πππ πππ’ ππππ§, ππβπ , πππ£π‘ππ ππππ§, ππβπ β πππ πππ’ πππ, ππππ§ , πππ πππ’ π2, π , πππ πππ’ πππ, πππ π π§ , πππ πππ’ πππ π π§, ππβπ , π‘ππππππ π1, π2 , π‘ππππππ ππππ§, πππ , π‘ππππππ πππ, πππ π π§ , π β π. ππβπ β πππ π π§. ππππ§ β ππβπ. β¦ πππ£π‘ππ πππ, πππ β πππ πππ’ πππ, πππ , πππ πππ’ πππ, πππ , π‘ππππππ πππ, πππ , πππ β πππ. β¦ Nick Hippen University of Nebraska at Omaha 4
Improving Performance Smaller grounding sizes often translate into faster solve times Idea: Split a logic rule into multiple rules so that the number of variables present in each new rule is smaller than that of the original. Projection Two types: π½ and πΎ Nick Hippen University of Nebraska at Omaha 5
PROJECTOR Result: π½ Logic Program PROJECTOR: π· -projection πππ£π‘ππ π, π β πππ πππ’ π1, π , π0 π, π1 β π‘ππππππ π1, π2 , πππ πππ’ π2, π . πππ πππ’ π2, π , π1 π, π β πππ πππ’ π1, π , π0 π, π1 . π‘ππππππ π1, π2 , πππ£π‘ππ π, π β π β π, π1 π, π . π β π. Nick Hippen University of Nebraska at Omaha 6
Nondeterministic behavior Logic Program PROJECTOR: π· -projection Scenario #1 PROJECTOR: π· -projection Scenario #2 πππ£π‘ππ π, π β πππ πππ’ π1, π , π0 π, π1 β π‘ππππππ π1, π2 , πππ πππ’ π2, π . π0 π2, π β π‘ππππππ π1, π2 , πππ πππ’ π1, π . πππ πππ’ π2, π , π1 π, π β πππ πππ’ π1, π , π0 π, π1 . π1 π, π β πππ πππ’ π2, π , π0 π2, π . π‘ππππππ π1, π2 , πππ£π‘ππ π, π β π β π, π1 π, π . πππ£π‘ππ π, π β π β π, π1 π, π . π β π. Nick Hippen University of Nebraska at Omaha 7
PROJECTOR Result: πΎ Logic Program PROJECTOR: π· -projection PROJECTOR: πΈ -projection ππππ β πππ£π‘ππ π, π β πππ πππ’ π1, π , π0 π, π1 β π‘ππππππ π1, π2 , πππ πππ’ π2, π . π0 π, π1 β π‘ππππππ π1, π2 , πππ πππ’ π2, π . πππ πππ’ π2, π , π1 π, π β πππ πππ’ π1, π , π0 π, π1 . π1 π, π β πππ πππ’ π1, π , π0 π, π1 , ππππ(π). π‘ππππππ π1, π2 , ππππ β πππ£π‘ππ π, π β π β π, ππππ π , π1 π, π . ππππ β πππ£π‘ππ π, π β π β π, ππππ π , π1 π, π . π β π ππππ(π). Nick Hippen University of Nebraska at Omaha 8
Experimental Analysis β’ ASPCCG : ASP based natural language parser β’ 3 encodings of increasing levels of human optimization β’ Created by Matthew Buddenhagen, Yuliya Lierler & Peter Schuller β’ Enc1: No human optimization β’ Enc7: Moderate human optimization β’ Enc19: Notable human optimization Nick Hippen University of Nebraska at Omaha 9
ASPCCG: Encoding 1 Solve Time Grounding Size Nick Hippen University of Nebraska at Omaha 10
ASPCCG: Encoding 7 Solve Time Grounding Size Nick Hippen University of Nebraska at Omaha 11
ASPCCG: Encoding 19 Solve Time Grounding Size Nick Hippen University of Nebraska at Omaha 12
ASPCCG: Overall Nick Hippen University of Nebraska at Omaha 13
Related, Current & Future Work β’ Related work: lpopt (Bichler, Morak, Woltran, 2016) β’ Paper will be submitted to Practical Aspects of Declarative Languages (PADL) 2019 this weekend β’ System PROJECTOR available on the UNO NLPKR Lab website Future Work β’ Gather more benchmarks β’ Grounding size prediction β’ Improve language support Nick Hippen University of Nebraska at Omaha 14
Acknowledgements β’ Michael Dingess β’ Brian Hodges β’ Daniel Houston β’ Roland Kaminski β’ Liu Liu β’ Dr. Mirek Truszczynski β’ Stefan Woltran Nick Hippen University of Nebraska at Omaha 15
Ques Questio ions? ns? Nick Hippen University of Nebraska at Omaha 16
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