PROJECTOR: an automatic logic program rewriting tool for better - - PowerPoint PPT Presentation

Nick Hippen University of Nebraska at Omaha

PROJECTOR: an automatic logic program rewriting tool for better performance

Nick Hippen & Yuliya Lierler

What is Answer Set Programming (ASP)?

• Constraint programming paradigm geared towards solving difficult

combinatorial search problems

• Prolog-like syntax

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Meaning X is a child of Y if Y is a parent of X. X is innocent if I have no reason to believe that X is guilty Logic Rule 𝑑ℎ𝑗𝑚𝑒 𝑌, 𝑍 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑍, 𝑌 . 𝑗𝑜𝑜𝑝𝑑𝑓𝑜𝑢 𝑌 ← 𝑜𝑝𝑢 𝑕𝑣𝑗𝑚𝑢𝑧 𝑌 . Head ← Body

ASP Solver Architecture

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PROJECTOR

logic program rewritten logic program

Grounder ASP Solver

grounded program answer sets logic program

Grounder ASP Solver

grounded program answer sets

Grounding Logic Programs

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Logic Program Grounded Program Intelligently Grounded Program 𝑞𝑏𝑠𝑓𝑜𝑢 𝑐𝑝𝑐, 𝑏𝑚𝑚𝑧 . 𝑞𝑏𝑠𝑓𝑜𝑢 𝑛𝑏𝑠𝑠𝑧, 𝑘𝑝ℎ𝑜 . 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑐𝑝𝑐, 𝑛𝑏𝑠𝑠𝑧 . 𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 , 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑌 ≠ 𝑍. 𝑞𝑏𝑠𝑓𝑜𝑢 𝑐𝑝𝑐, 𝑏𝑚𝑚𝑧 . 𝑞𝑏𝑠𝑓𝑜𝑢 𝑛𝑏𝑠𝑠𝑧, 𝑘𝑝ℎ𝑜 . 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑐𝑝𝑐, 𝑛𝑏𝑠𝑠𝑧 . 𝑑𝑝𝑣𝑡𝑗𝑜 𝑘𝑝ℎ𝑜, 𝑛𝑏𝑠𝑠𝑧 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑏𝑚𝑚𝑧, 𝑘𝑝ℎ𝑜 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑐𝑝𝑐, 𝑛𝑏𝑠𝑠𝑧 , 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑏𝑚𝑚𝑧, 𝑐𝑝𝑐 , 𝑘𝑝ℎ𝑜 ≠ 𝑛𝑏𝑠𝑠𝑧. … 𝑑𝑝𝑣𝑡𝑗𝑜 𝑐𝑝𝑐, 𝑐𝑝𝑐 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑐𝑝𝑐, 𝑐𝑝𝑐 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑐𝑝𝑐, 𝑐𝑝𝑐 , 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑐𝑝𝑐, 𝑐𝑝𝑐 , 𝑐𝑝𝑐 ≠ 𝑐𝑝𝑐. … 𝑞𝑏𝑠𝑓𝑜𝑢 𝑐𝑝𝑐, 𝑏𝑚𝑚𝑧 . 𝑞𝑏𝑠𝑓𝑜𝑢 𝑛𝑏𝑠𝑠𝑧, 𝑘𝑝ℎ𝑜 . 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑐𝑝𝑐, 𝑛𝑏𝑠𝑠𝑧 . 𝑑𝑝𝑣𝑡𝑗𝑜 𝑏𝑚𝑚𝑧, 𝑘𝑝ℎ𝑜 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑐𝑝𝑐, 𝑏𝑚𝑚𝑧 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑛𝑏𝑠𝑠𝑧, 𝑘𝑝ℎ𝑜 , 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑐𝑝𝑐, 𝑛𝑏𝑠𝑠𝑧 , 𝑏𝑚𝑚𝑧 ≠ 𝑘𝑝ℎ𝑜.

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: 𝛽 and 𝛾

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PROJECTOR Result: 𝛽

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Logic Program PROJECTOR: 𝜷-projection 𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 , 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑌 ≠ 𝑍. 𝑞0 𝑍, 𝑄1 ← 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 . 𝑞1 𝑍, 𝑌 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 , 𝑞0 𝑍, 𝑄1 . 𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑌 ≠ 𝑍, 𝑞1 𝑍, 𝑌 .

Nondeterministic behavior

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Logic Program PROJECTOR: 𝜷-projection Scenario #1 PROJECTOR: 𝜷-projection Scenario #2 𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 , 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑌 ≠ 𝑍. 𝑞0 𝑍, 𝑄1 ← 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 . 𝑞1 𝑍, 𝑌 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 , 𝑞0 𝑍, 𝑄1 . 𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑌 ≠ 𝑍, 𝑞1 𝑍, 𝑌 . 𝑞0 𝑄2, 𝑌 ← 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 . 𝑞1 𝑍, 𝑌 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 , 𝑞0 𝑄2, 𝑌 . 𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑌 ≠ 𝑍, 𝑞1 𝑍, 𝑌 .

PROJECTOR Result: 𝛾

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Logic Program PROJECTOR: 𝜷-projection PROJECTOR: 𝜸-projection 𝑛𝑏𝑚𝑓↓𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 , 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑌 ≠ 𝑍 𝑛𝑏𝑚𝑓(𝑌). 𝑞0 𝑍, 𝑄1 ← 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 . 𝑞1 𝑍, 𝑌 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 , 𝑞0 𝑍, 𝑄1 . 𝑛𝑏𝑚𝑓↓𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑌 ≠ 𝑍, 𝑛𝑏𝑚𝑓 𝑌 , 𝑞1 𝑍, 𝑌 . 𝑞0 𝑍, 𝑄1 ← 𝑡𝑗𝑐𝑚𝑗𝑜𝑕 𝑄1, 𝑄2 , 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄2, 𝑍 . 𝑞1 𝑍, 𝑌 ← 𝑞𝑏𝑠𝑓𝑜𝑢 𝑄1, 𝑌 , 𝑞0 𝑍, 𝑄1 , 𝑛𝑏𝑚𝑓(𝑌). 𝑛𝑏𝑚𝑓↓𝑑𝑝𝑣𝑡𝑗𝑜 𝑌, 𝑍 ← 𝑌 ≠ 𝑍, 𝑛𝑏𝑚𝑓 𝑌 , 𝑞1 𝑍, 𝑌 .

Experimental Analysis

• ASPCCG: ASP based natural language parser
• 3 encodings of increasing levels of human optimization
• Created by Matthew Buddenhagen, Yuliya Lierler & Peter Schuller
• Enc1: No human optimization
• Enc7: Moderate human optimization
• Enc19: Notable human optimization

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ASPCCG: Encoding 1

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Solve Time Grounding Size

ASPCCG: Encoding 7

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Solve Time Grounding Size

ASPCCG: Encoding 19

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Solve Time Grounding Size

ASPCCG: Overall

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Related, Current & Future Work

• Related work: lpopt (Bichler, Morak, Woltran, 2016)
• Paper will be submitted to Practical Aspects of Declarative Languages (PADL) 2019 this weekend
• System PROJECTOR available on the UNO NLPKR Lab website

Future Work

• Gather more benchmarks
• Grounding size prediction
• Improve language support

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Acknowledgements

• Michael Dingess
• Brian Hodges
• Daniel Houston
• Roland Kaminski
• Liu Liu
• Dr. Mirek Truszczynski
• Stefan Woltran

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Ques Questio ions? ns?

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