Video Converter
Audio Converter
Image Converter
PDF Converter
File Compressor
answer set solving in practice

Answer Set Solving in Practice Torsten Schaub University of Potsdam - PowerPoint PPT Presentation

Sep 12, 2023 •324 likes •1.67k views

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

  1. ASP solving process Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     Problem edge(3,1). edge(3,4). edge(3,5).  instance edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N). Problem  encoding :- edge(N,M), assign(N,C), assign(M,C).  Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 66 / 541

  2. ASP solving process Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     Problem edge(3,1). edge(3,4). edge(3,5).  instance edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N). Problem  encoding :- edge(N,M), assign(N,C), assign(M,C).  Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 66 / 541

  3. ASP solving process Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     Problem edge(3,1). edge(3,4). edge(3,5).  instance edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N). Problem  encoding :- edge(N,M), assign(N,C), assign(M,C).  Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 66 / 541

  4. ASP solving process Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     Problem edge(3,1). edge(3,4). edge(3,5).  instance edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N). Problem  encoding :- edge(N,M), assign(N,C), assign(M,C).  Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 66 / 541

  5. ASP solving process Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     Problem edge(3,1). edge(3,4). edge(3,5).  instance edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N). Problem  encoding :- edge(N,M), assign(N,C), assign(M,C).  Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 66 / 541

  6. ASP solving process Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     edge(3,1). edge(3,4). edge(3,5).  graph.lp edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N).   color.lp :- edge(N,M), assign(N,C), assign(M,C). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 66 / 541

  7. ASP solving process ASP solving process Problem Solution ✻ Modeling Interpreting ❄ Logic ✲ ✲ ✲ Stable Grounder Solver Program Models Solving Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 67 / 541

  8. ASP solving process Graph coloring: Grounding $ gringo --text graph.lp color.lp node(1). node(2). node(3). node(4). node(5). node(6). edge(1,2). edge(2,4). edge(3,1). edge(4,1). edge(5,3). edge(6,2). edge(1,3). edge(2,5). edge(3,4). edge(4,2). edge(5,4). edge(6,3). edge(1,4). edge(2,6). edge(3,5). edge(5,6). edge(6,5). color(r). color(b). color(g). { assign(1,r), assign(1,b), assign(1,g) } = 1. { assign(4,r), assign(4,b), assign(4,g) } = 1. { assign(2,r), assign(2,b), assign(2,g) } = 1. { assign(5,r), assign(5,b), assign(5,g) } = 1. { assign(3,r), assign(3,b), assign(3,g) } = 1. { assign(6,r), assign(6,b), assign(6,g) } = 1. :- assign(1,r), assign(2,r). :- assign(2,r), assign(4,r). [...] :- assign(6,r), assign(2,r). :- assign(1,b), assign(2,b). :- assign(2,b), assign(4,b). :- assign(6,b), assign(2,b). :- assign(1,g), assign(2,g). :- assign(2,g), assign(4,g). :- assign(6,g), assign(2,g). :- assign(1,r), assign(3,r). :- assign(2,r), assign(5,r). :- assign(6,r), assign(3,r). :- assign(1,b), assign(3,b). :- assign(2,b), assign(5,b). :- assign(6,b), assign(3,b). :- assign(1,g), assign(3,g). :- assign(2,g), assign(5,g). :- assign(6,g), assign(3,g). :- assign(1,r), assign(4,r). :- assign(2,r), assign(6,r). :- assign(6,r), assign(5,r). :- assign(1,b), assign(4,b). :- assign(2,b), assign(6,b). :- assign(6,b), assign(5,b). :- assign(1,g), assign(4,g). :- assign(2,g), assign(6,g). :- assign(6,g), assign(5,g). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 68 / 541

  9. ASP solving process Graph coloring: Grounding $ gringo --text graph.lp color.lp node(1). node(2). node(3). node(4). node(5). node(6). edge(1,2). edge(2,4). edge(3,1). edge(4,1). edge(5,3). edge(6,2). edge(1,3). edge(2,5). edge(3,4). edge(4,2). edge(5,4). edge(6,3). edge(1,4). edge(2,6). edge(3,5). edge(5,6). edge(6,5). color(r). color(b). color(g). { assign(1,r), assign(1,b), assign(1,g) } = 1. { assign(4,r), assign(4,b), assign(4,g) } = 1. { assign(2,r), assign(2,b), assign(2,g) } = 1. { assign(5,r), assign(5,b), assign(5,g) } = 1. { assign(3,r), assign(3,b), assign(3,g) } = 1. { assign(6,r), assign(6,b), assign(6,g) } = 1. :- assign(1,r), assign(2,r). :- assign(2,r), assign(4,r). [...] :- assign(6,r), assign(2,r). :- assign(1,b), assign(2,b). :- assign(2,b), assign(4,b). :- assign(6,b), assign(2,b). :- assign(1,g), assign(2,g). :- assign(2,g), assign(4,g). :- assign(6,g), assign(2,g). :- assign(1,r), assign(3,r). :- assign(2,r), assign(5,r). :- assign(6,r), assign(3,r). :- assign(1,b), assign(3,b). :- assign(2,b), assign(5,b). :- assign(6,b), assign(3,b). :- assign(1,g), assign(3,g). :- assign(2,g), assign(5,g). :- assign(6,g), assign(3,g). :- assign(1,r), assign(4,r). :- assign(2,r), assign(6,r). :- assign(6,r), assign(5,r). :- assign(1,b), assign(4,b). :- assign(2,b), assign(6,b). :- assign(6,b), assign(5,b). :- assign(1,g), assign(4,g). :- assign(2,g), assign(6,g). :- assign(6,g), assign(5,g). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 68 / 541

  10. ASP solving process Graph coloring: Grounding $ gringo --text graph.lp color.lp node(1). node(2). node(3). node(4). node(5). node(6). edge(1,2). edge(2,4). edge(3,1). edge(4,1). edge(5,3). edge(6,2). edge(1,3). edge(2,5). edge(3,4). edge(4,2). edge(5,4). edge(6,3). edge(1,4). edge(2,6). edge(3,5). edge(5,6). edge(6,5). color(r). color(b). color(g). { assign(1,r), assign(1,b), assign(1,g) } = 1. { assign(4,r), assign(4,b), assign(4,g) } = 1. { assign(2,r), assign(2,b), assign(2,g) } = 1. { assign(5,r), assign(5,b), assign(5,g) } = 1. { assign(3,r), assign(3,b), assign(3,g) } = 1. { assign(6,r), assign(6,b), assign(6,g) } = 1. :- assign(1,r), assign(2,r). :- assign(2,r), assign(4,r). [...] :- assign(6,r), assign(2,r). :- assign(1,b), assign(2,b). :- assign(2,b), assign(4,b). :- assign(6,b), assign(2,b). :- assign(1,g), assign(2,g). :- assign(2,g), assign(4,g). :- assign(6,g), assign(2,g). :- assign(1,r), assign(3,r). :- assign(2,r), assign(5,r). :- assign(6,r), assign(3,r). :- assign(1,b), assign(3,b). :- assign(2,b), assign(5,b). :- assign(6,b), assign(3,b). :- assign(1,g), assign(3,g). :- assign(2,g), assign(5,g). :- assign(6,g), assign(3,g). :- assign(1,r), assign(4,r). :- assign(2,r), assign(6,r). :- assign(6,r), assign(5,r). :- assign(1,b), assign(4,b). :- assign(2,b), assign(6,b). :- assign(6,b), assign(5,b). :- assign(1,g), assign(4,g). :- assign(2,g), assign(6,g). :- assign(6,g), assign(5,g). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 68 / 541

  11. ASP solving process Graph coloring: Grounding $ gringo --text graph.lp color.lp node(1). node(2). node(3). node(4). node(5). node(6). edge(1,2). edge(2,4). edge(3,1). edge(4,1). edge(5,3). edge(6,2). edge(1,3). edge(2,5). edge(3,4). edge(4,2). edge(5,4). edge(6,3). edge(1,4). edge(2,6). edge(3,5). edge(5,6). edge(6,5). color(r). color(b). color(g). { assign(1,r), assign(1,b), assign(1,g) } = 1. { assign(4,r), assign(4,b), assign(4,g) } = 1. { assign(2,r), assign(2,b), assign(2,g) } = 1. { assign(5,r), assign(5,b), assign(5,g) } = 1. { assign(3,r), assign(3,b), assign(3,g) } = 1. { assign(6,r), assign(6,b), assign(6,g) } = 1. :- assign(1,r), assign(2,r). :- assign(2,r), assign(4,r). [...] :- assign(6,r), assign(2,r). :- assign(1,b), assign(2,b). :- assign(2,b), assign(4,b). :- assign(6,b), assign(2,b). :- assign(1,g), assign(2,g). :- assign(2,g), assign(4,g). :- assign(6,g), assign(2,g). :- assign(1,r), assign(3,r). :- assign(2,r), assign(5,r). :- assign(6,r), assign(3,r). :- assign(1,b), assign(3,b). :- assign(2,b), assign(5,b). :- assign(6,b), assign(3,b). :- assign(1,g), assign(3,g). :- assign(2,g), assign(5,g). :- assign(6,g), assign(3,g). :- assign(1,r), assign(4,r). :- assign(2,r), assign(6,r). :- assign(6,r), assign(5,r). :- assign(1,b), assign(4,b). :- assign(2,b), assign(6,b). :- assign(6,b), assign(5,b). :- assign(1,g), assign(4,g). :- assign(2,g), assign(6,g). :- assign(6,g), assign(5,g). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 68 / 541

  12. ASP solving process Graph coloring: Grounding $ clingo --text graph.lp color.lp node(1). node(2). node(3). node(4). node(5). node(6). edge(1,2). edge(2,4). edge(3,1). edge(4,1). edge(5,3). edge(6,2). edge(1,3). edge(2,5). edge(3,4). edge(4,2). edge(5,4). edge(6,3). edge(1,4). edge(2,6). edge(3,5). edge(5,6). edge(6,5). color(r). color(b). color(g). { assign(1,r), assign(1,b), assign(1,g) } = 1. { assign(4,r), assign(4,b), assign(4,g) } = 1. { assign(2,r), assign(2,b), assign(2,g) } = 1. { assign(5,r), assign(5,b), assign(5,g) } = 1. { assign(3,r), assign(3,b), assign(3,g) } = 1. { assign(6,r), assign(6,b), assign(6,g) } = 1. :- assign(1,r), assign(2,r). :- assign(2,r), assign(4,r). [...] :- assign(6,r), assign(2,r). :- assign(1,b), assign(2,b). :- assign(2,b), assign(4,b). :- assign(6,b), assign(2,b). :- assign(1,g), assign(2,g). :- assign(2,g), assign(4,g). :- assign(6,g), assign(2,g). :- assign(1,r), assign(3,r). :- assign(2,r), assign(5,r). :- assign(6,r), assign(3,r). :- assign(1,b), assign(3,b). :- assign(2,b), assign(5,b). :- assign(6,b), assign(3,b). :- assign(1,g), assign(3,g). :- assign(2,g), assign(5,g). :- assign(6,g), assign(3,g). :- assign(1,r), assign(4,r). :- assign(2,r), assign(6,r). :- assign(6,r), assign(5,r). :- assign(1,b), assign(4,b). :- assign(2,b), assign(6,b). :- assign(6,b), assign(5,b). :- assign(1,g), assign(4,g). :- assign(2,g), assign(6,g). :- assign(6,g), assign(5,g). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 68 / 541

  13. ASP solving process ASP solving process Problem Solution ✻ Modeling Interpreting ❄ Logic ✲ ✲ ✲ Stable Grounder Solver Program Models Solving Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 69 / 541

  14. ASP solving process Graph coloring: Solving $ gringo graph.lp color.lp | clasp 0 clasp version 2.1.0 Reading from stdin Solving... Answer: 1 node(1) [...] assign(6,b) assign(5,g) assign(4,b) assign(3,r) assign(2,r) assign(1,g) Answer: 2 node(1) [...] assign(6,r) assign(5,g) assign(4,r) assign(3,b) assign(2,b) assign(1,g) Answer: 3 node(1) [...] assign(6,g) assign(5,b) assign(4,g) assign(3,r) assign(2,r) assign(1,b) Answer: 4 node(1) [...] assign(6,r) assign(5,b) assign(4,r) assign(3,g) assign(2,g) assign(1,b) Answer: 5 node(1) [...] assign(6,g) assign(5,r) assign(4,g) assign(3,b) assign(2,b) assign(1,r) Answer: 6 node(1) [...] assign(6,b) assign(5,r) assign(4,b) assign(3,g) assign(2,g) assign(1,r) SATISFIABLE Models : 6 Time : 0.002s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 70 / 541

  15. ASP solving process Graph coloring: Solving $ gringo graph.lp color.lp | clasp 0 clasp version 2.1.0 Reading from stdin Solving... Answer: 1 node(1) [...] assign(6,b) assign(5,g) assign(4,b) assign(3,r) assign(2,r) assign(1,g) Answer: 2 node(1) [...] assign(6,r) assign(5,g) assign(4,r) assign(3,b) assign(2,b) assign(1,g) Answer: 3 node(1) [...] assign(6,g) assign(5,b) assign(4,g) assign(3,r) assign(2,r) assign(1,b) Answer: 4 node(1) [...] assign(6,r) assign(5,b) assign(4,r) assign(3,g) assign(2,g) assign(1,b) Answer: 5 node(1) [...] assign(6,g) assign(5,r) assign(4,g) assign(3,b) assign(2,b) assign(1,r) Answer: 6 node(1) [...] assign(6,b) assign(5,r) assign(4,b) assign(3,g) assign(2,g) assign(1,r) SATISFIABLE Models : 6 Time : 0.002s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 70 / 541

  16. ASP solving process Graph coloring: Solving $ clingo graph.lp color.lp 0 clasp version 2.1.0 Reading from stdin Solving... Answer: 1 node(1) [...] assign(6,b) assign(5,g) assign(4,b) assign(3,r) assign(2,r) assign(1,g) Answer: 2 node(1) [...] assign(6,r) assign(5,g) assign(4,r) assign(3,b) assign(2,b) assign(1,g) Answer: 3 node(1) [...] assign(6,g) assign(5,b) assign(4,g) assign(3,r) assign(2,r) assign(1,b) Answer: 4 node(1) [...] assign(6,r) assign(5,b) assign(4,r) assign(3,g) assign(2,g) assign(1,b) Answer: 5 node(1) [...] assign(6,g) assign(5,r) assign(4,g) assign(3,b) assign(2,b) assign(1,r) Answer: 6 node(1) [...] assign(6,b) assign(5,r) assign(4,b) assign(3,g) assign(2,g) assign(1,r) SATISFIABLE Models : 6 Time : 0.002s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 70 / 541

  17. ASP solving process ASP solving process Problem Solution ✻ Modeling Interpreting ❄ Logic ✲ ✲ ✲ Stable Grounder Solver Program Models Solving Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 71 / 541

  18. ASP solving process A coloring Answer: 6 node(1) [...] \ assign(6,b) assign(5,r) assign(4,b) assign(3,g) assign(2,g) assign(1,r) 3 5 6 1 2 4 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 72 / 541

  19. ASP solving process A coloring Answer: 6 node(1) [...] \ assign(6,b) assign(5,r) assign(4,b) assign(3,g) assign(2,g) assign(1,r) 3 5 6 1 2 4 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 72 / 541

  20. Methodology Outline 1 Elaboration tolerance 2 ASP solving process 3 Methodology 4 Case studies Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 73 / 541

  21. Methodology Basic methodology Methodology Generate and Test (or: Guess and Check) Generator Generate potential stable model candidates (typically through non-deterministic constructs) Tester Eliminate invalid candidates (typically through integrity constraints) Nutshell Logic program = Data + Generator + Tester ( + Optimizer) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 74 / 541

  22. Methodology Basic methodology Methodology Generate and Test (or: Guess and Check) Generator Generate potential stable model candidates (typically through non-deterministic constructs) Tester Eliminate invalid candidates (typically through integrity constraints) Nutshell Logic program = Data + Generator + Tester ( + Optimizer) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 74 / 541

  23. Methodology Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     Problem edge(3,1). edge(3,4). edge(3,5).  instance edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N). Problem  encoding :- edge(N,M), assign(N,C), assign(M,C).  Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 75 / 541

  24. Methodology Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     edge(3,1). edge(3,4). edge(3,5).  Data edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N). Problem  encoding :- edge(N,M), assign(N,C), assign(M,C).  Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 75 / 541

  25. Methodology Graph coloring node(1..6).        edge(1,2). edge(1,3). edge(1,4).     edge(2,4). edge(2,5). edge(2,6).     edge(3,1). edge(3,4). edge(3,5).  Data edge(4,1). edge(4,2).   edge(5,3). edge(5,4). edge(5,6).     edge(6,2). edge(6,3). edge(6,5).         color(r). color(b). color(g).   { assign(N,C) : color(C) } = 1 :- node(N). Generator  Tester :- edge(N,M), assign(N,C), assign(M,C).  Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 75 / 541

  26. Case studies Outline 1 Elaboration tolerance 2 ASP solving process 3 Methodology 4 Case studies Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 76 / 541

  27. Case studies Satisfiability Outline 1 Elaboration tolerance 2 ASP solving process 3 Methodology 4 Case studies Satisfiability Queens Traveling salesperson Reviewer Assignment Planning Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 77 / 541

  28. Case studies Satisfiability Satisfiability testing Problem Instance A propositional formula φ in CNF Problem Class Is there an assignment of propositional variables to true and false such that a given formula φ is true Example: Consider formula ( a ∨ ¬ b ) ∧ ( ¬ a ∨ b ) Logic Program Generator Tester Stable models { a } ← ← ∼ a , b X 1 = { a , b } { b } ← ← a , ∼ b X 2 = {} Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 78 / 541

  29. Case studies Satisfiability Satisfiability testing Problem Instance A propositional formula φ in CNF Problem Class Is there an assignment of propositional variables to true and false such that a given formula φ is true Example: Consider formula ( a ∨ ¬ b ) ∧ ( ¬ a ∨ b ) Logic Program Generator Tester Stable models { a } ← ← ∼ a , b X 1 = { a , b } { b } ← ← a , ∼ b X 2 = {} Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 78 / 541

  30. Case studies Satisfiability Satisfiability testing Problem Instance A propositional formula φ in CNF Problem Class Is there an assignment of propositional variables to true and false such that a given formula φ is true Example: Consider formula ( a ∨ ¬ b ) ∧ ( ¬ a ∨ b ) Logic Program Generator Tester Stable models { a } ← ← ∼ a , b X 1 = { a , b } { b } ← ← a , ∼ b X 2 = {} Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 78 / 541

  31. Case studies Satisfiability Satisfiability testing Problem Instance A propositional formula φ in CNF Problem Class Is there an assignment of propositional variables to true and false such that a given formula φ is true Example: Consider formula ( a ∨ ¬ b ) ∧ ( ¬ a ∨ b ) Logic Program Generator Tester Stable models { a } ← ← ∼ a , b X 1 = { a , b } { b } ← ← a , ∼ b X 2 = {} Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 78 / 541

  32. Case studies Satisfiability Satisfiability testing Problem Instance A propositional formula φ in CNF Problem Class Is there an assignment of propositional variables to true and false such that a given formula φ is true Example: Consider formula ( a ∨ ¬ b ) ∧ ( ¬ a ∨ b ) Logic Program Generator Tester Stable models { a } ← ← ∼ a , b X 1 = { a , b } { b } ← ← a , ∼ b X 2 = {} Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 78 / 541

  33. Case studies Queens Outline 1 Elaboration tolerance 2 ASP solving process 3 Methodology 4 Case studies Satisfiability Queens Traveling salesperson Reviewer Assignment Planning Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 79 / 541

  34. Case studies Queens The n-queens problem 5 Z0Z0Z 4 0Z0Z0 Place n queens on an n × n chess board Queens must not attack one another 3 Z0Z0Z 2 0Z0Z0 Q Q Q 1 Z0Z0Z Q Q 1 2 3 4 5 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 80 / 541

  35. Case studies Queens Defining the field queens.lp row(1..n). col(1..n). Create file queens.lp Define the field n rows n columns Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 81 / 541

  36. Case studies Queens Defining the field Running . . . $ clingo queens.lp --const n=5 Answer: 1 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) SATISFIABLE Models : 1 Time : 0.000 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 82 / 541

  37. Case studies Queens Placing some queens queens.lp row(1..n). col(1..n). { queen(I,J) : row(I), col(J) } . Guess a solution candidate by placing some queens on the board Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 83 / 541

  38. Case studies Queens Placing some queens Running . . . $ clingo queens.lp --const n=5 3 Answer: 1 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) Answer: 2 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) queen(1,1) Answer: 3 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) queen(2,1) SATISFIABLE Models : 3+ Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 84 / 541

  39. Case studies Queens Placing some queens Answer: 1 5 Z0Z0Z 4 0Z0Z0 3 Z0Z0Z 2 0Z0Z0 Answer: 1 row(1) row(2) row(3) row(4) row(5) \ 1 Z0Z0Z col(1) col(2) col(3) col(4) col(5) 1 2 3 4 5 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 85 / 541

  40. Case studies Queens Placing some queens Answer: 2 5 Z0Z0Z 4 0Z0Z0 3 Z0Z0Z 2 0Z0Z0 Answer: 2 row(1) row(2) row(3) row(4) row(5) \ 1 L0Z0Z col(1) col(2) col(3) col(4) col(5) \ queen(1,1) 1 2 3 4 5 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 86 / 541

  41. Case studies Queens Placing some queens Answer: 3 5 Z0Z0Z 4 0Z0Z0 3 Z0Z0Z 2 QZ0Z0 Answer: 3 row(1) row(2) row(3) row(4) row(5) \ 1 Z0Z0Z col(1) col(2) col(3) col(4) col(5) \ queen(2,1) 1 2 3 4 5 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 87 / 541

  42. Case studies Queens Placing n queens queens.lp row(1..n). col(1..n). { queen(I,J) : row(I), col(J) }. :- { queen(I,J) } != n. Place exactly n queens on the board Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 88 / 541

  43. Case studies Queens Placing n queens queens.lp row(1..n). col(1..n). { queen(I,J) : row(I), col(J) }. :- not { queen(I,J) } = n. Place exactly n queens on the board Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 88 / 541

  44. Case studies Queens Placing n queens Running . . . $ clingo queens.lp --const n=5 2 Answer: 1 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) \ queen(5,1) queen(4,1) queen(3,1) queen(2,1) queen(1,1) Answer: 2 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) \ queen(1,2) queen(4,1) queen(3,1) queen(2,1) queen(1,1) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 89 / 541

  45. Case studies Queens Placing n queens Answer: 1 5 L0Z0Z 4 QZ0Z0 3 L0Z0Z Answer: 1 2 QZ0Z0 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) \ 1 L0Z0Z queen(5,1) queen(4,1) queen(3,1) queen(2,1) queen(1,1) 1 2 3 4 5 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 90 / 541

  46. Case studies Queens Placing n queens Answer: 2 5 Z0Z0Z 4 QZ0Z0 3 L0Z0Z Answer: 2 2 QZ0Z0 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) \ 1 LQZ0Z queen(1,2) queen(4,1) queen(3,1) queen(2,1) queen(1,1) 1 2 3 4 5 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 91 / 541

  47. Case studies Queens Horizontal and vertical attack queens.lp row(1..n). col(1..n). { queen(I,J) : row(I), col(J) }. :- { queen(I,J) } != n. :- queen(I,J), queen(I,J’), J != J’. :- queen(I,J), queen(I’,J), I != I’. Forbid horizontal attacks Forbid vertical attacks Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 92 / 541

  48. Case studies Queens Horizontal and vertical attack queens.lp row(1..n). col(1..n). { queen(I,J) : row(I), col(J) }. :- { queen(I,J) } != n. :- queen(I,J), queen(I,J’), J != J’. :- queen(I,J), queen(I’,J), I != I’. Forbid horizontal attacks Forbid vertical attacks Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 92 / 541

  49. Case studies Queens Horizontal and vertical attack Running . . . $ clingo queens.lp --const n=5 Answer: 1 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) \ queen(5,5) queen(4,4) queen(3,3) queen(2,2) queen(1,1) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 93 / 541

  50. Case studies Queens Horizontal and vertical attack Answer: 1 5 Z0Z0L 4 0Z0L0 3 Z0L0Z Answer: 1 2 0L0Z0 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) \ 1 L0Z0Z queen(5,5) queen(4,4) queen(3,3) queen(2,2) queen(1,1) 1 2 3 4 5 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 94 / 541

  51. Case studies Queens Diagonal attack queens.lp row(1..n). col(1..n). { queen(I,J) : row(I), col(J) }. :- { queen(I,J) } != n. :- queen(I,J), queen(I,J’), J != J’. :- queen(I,J), queen(I’,J), I != I’. :- queen(I,J), queen(I’,J’), (I,J) != (I’,J’), I-J == I’-J’. :- queen(I,J), queen(I’,J’), (I,J) != (I’,J’), I+J == I’+J’. Forbid diagonal attacks Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 95 / 541

  52. Case studies Queens Diagonal attack Running . . . $ clingo queens.lp --const n=5 Answer: 1 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) \ queen(4,5) queen(1,4) queen(3,3) queen(5,2) queen(2,1) SATISFIABLE Models : 1+ Time : 0.000 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 96 / 541

  53. Case studies Queens Diagonal attack Answer: 1 5 ZQZ0Z 4 0Z0ZQ 3 Z0L0Z Answer: 1 2 QZ0Z0 row(1) row(2) row(3) row(4) row(5) \ col(1) col(2) col(3) col(4) col(5) \ 1 Z0ZQZ queen(4,5) queen(1,4) queen(3,3) queen(5,2) queen(2,1) 1 2 3 4 5 Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 97 / 541

  54. Case studies Queens Optimizing queens-opt.lp { queen(I,1..n) } = 1 :- I = 1..n. { queen(1..n,J) } = 1 :- J = 1..n. :- { queen(D-J,J) } > 1, D = 2..2*n. :- { queen(D+J,J) } > 1, D = 1-n..n-1. Encoding can be optimized Much faster to solve Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 98 / 541

  55. Case studies Queens And sometimes it rocks $ clingo -c n=5000 queens-opt-diag.lp --config=jumpy -q --stats=2 clingo version 4.1.0 Solving... SATISFIABLE Models : 1+ Time : 3758.143s (Solving: 1905.22s 1st Model: 1896.20s Unsat: 0.00s) CPU Time : 3758.320s Choices : 288594554 Conflicts : 3442 (Analyzed: 3442) Restarts : 17 (Average: 202.47 Last: 3442) Model-Level : 7594728.0 Problems : 1 (Average Length: 0.00 Splits: 0) Lemmas : 3442 (Deleted: 0) Binary : 0 (Ratio: 0.00%) Ternary : 0 (Ratio: 0.00%) Conflict : 3442 (Average Length: 229056.5 Ratio: 100.00%) Loop : 0 (Average Length: 0.0 Ratio: 0.00%) Other : 0 (Average Length: 0.0 Ratio: 0.00%) Atoms : 75084857 (Original: 75069989 Auxiliary: 14868) Rules : 100129956 (1: 50059992/100090100 2: 39990/29856 3: 10000/10000) Bodies : 25090103 Equivalences : 125029999 (Atom=Atom: 50009999 Body=Body: 0 Other: 75020000) Tight : Yes Variables : 25024868 (Eliminated: 11781 Frozen: 25000000) Constraints : 66664 (Binary: 35.6% Ternary: 0.0% Other: 64.4%) Backjumps : 3442 (Average: 681.19 Max: 169512 Sum: 2344658) Executed : 3442 (Average: 681.19 Max: 169512 Sum: 2344658 Ratio: 100.00%) Bounded : 0 (Average: 0.00 Max: 0 Sum: 0 Ratio: 0.00%) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 99 / 541

  56. Case studies Queens And sometimes it rocks $ clingo -c n=5000 queens-opt-diag.lp --config=jumpy -q --stats=2 clingo version 4.1.0 Solving... SATISFIABLE Models : 1+ Time : 3758.143s (Solving: 1905.22s 1st Model: 1896.20s Unsat: 0.00s) CPU Time : 3758.320s Choices : 288594554 Conflicts : 3442 (Analyzed: 3442) Restarts : 17 (Average: 202.47 Last: 3442) Model-Level : 7594728.0 Problems : 1 (Average Length: 0.00 Splits: 0) Lemmas : 3442 (Deleted: 0) Binary : 0 (Ratio: 0.00%) Ternary : 0 (Ratio: 0.00%) Conflict : 3442 (Average Length: 229056.5 Ratio: 100.00%) Loop : 0 (Average Length: 0.0 Ratio: 0.00%) Other : 0 (Average Length: 0.0 Ratio: 0.00%) Atoms : 75084857 (Original: 75069989 Auxiliary: 14868) Rules : 100129956 (1: 50059992/100090100 2: 39990/29856 3: 10000/10000) Bodies : 25090103 Equivalences : 125029999 (Atom=Atom: 50009999 Body=Body: 0 Other: 75020000) Tight : Yes Variables : 25024868 (Eliminated: 11781 Frozen: 25000000) Constraints : 66664 (Binary: 35.6% Ternary: 0.0% Other: 64.4%) Backjumps : 3442 (Average: 681.19 Max: 169512 Sum: 2344658) Executed : 3442 (Average: 681.19 Max: 169512 Sum: 2344658 Ratio: 100.00%) Bounded : 0 (Average: 0.00 Max: 0 Sum: 0 Ratio: 0.00%) Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 99 / 541

  57. Case studies Traveling salesperson Outline 1 Elaboration tolerance 2 ASP solving process 3 Methodology 4 Case studies Satisfiability Queens Traveling salesperson Reviewer Assignment Planning Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 100 / 541

  58. Case studies Traveling salesperson The traveling salesperson problem (TSP) Problem Instance A set of cities and distances among them, or simply a weighted graph Problem Class What is the shortest possible route visiting each city and returning to the city of origin? Note TSP extends the Hamiltonian cycle problem: Is there a cycle in a graph visiting each node exactly once TSP is relevant to applications in logistics, planning, chip design, and the core of the vehicle routing problem Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 101 / 541

  59. Case studies Traveling salesperson The traveling salesperson problem (TSP) Problem Instance A set of cities and distances among them, or simply a weighted graph Problem Class What is the shortest possible route visiting each city and returning to the city of origin? Note TSP extends the Hamiltonian cycle problem: Is there a cycle in a graph visiting each node exactly once TSP is relevant to applications in logistics, planning, chip design, and the core of the vehicle routing problem Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 101 / 541

  60. Case studies Traveling salesperson Traveling salesperson node(1..6). edge(1,(2;3;4)). edge(2,(4;5;6)). edge(3,(1;4;5)). edge(4,(1;2)). edge(5,(3;4;6)). edge(6,(2;3;5)). cost(1,2,2). cost(1,3,3). cost(1,4,1). cost(2,4,2). cost(2,5,2). cost(2,6,4). cost(3,1,3). cost(3,4,2). cost(3,5,2). cost(4,1,1). cost(4,2,2). cost(5,3,2). cost(5,4,2). cost(5,6,1). cost(6,2,4). cost(6,3,3). cost(6,5,1). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 102 / 541

  61. Case studies Traveling salesperson Traveling salesperson node(1..6). edge(1,(2;3;4)). edge(2,(4;5;6)). edge(3,(1;4;5)). edge(4,(1;2)). edge(5,(3;4;6)). edge(6,(2;3;5)). cost(1,2,2). cost(1,3,3). cost(1,4,1). cost(2,4,2). cost(2,5,2). cost(2,6,4). cost(3,1,3). cost(3,4,2). cost(3,5,2). cost(4,1,1). cost(4,2,2). cost(5,3,2). cost(5,4,2). cost(5,6,1). cost(6,2,4). cost(6,3,3). cost(6,5,1). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 102 / 541

  62. Case studies Traveling salesperson Traveling salesperson node(1..6). edge(1,(2;3;4)). edge(2,(4;5;6)). edge(3,(1;4;5)). edge(4,(1;2)). edge(5,(3;4;6)). edge(6,(2;3;5)). cost(1,2,2). cost(1,3,3). cost(1,4,1). cost(2,4,2). cost(2,5,2). cost(2,6,4). cost(3,1,3). cost(3,4,2). cost(3,5,2). cost(4,1,1). cost(4,2,2). cost(5,3,2). cost(5,4,2). cost(5,6,1). cost(6,2,4). cost(6,3,3). cost(6,5,1). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 102 / 541

  63. Case studies Traveling salesperson Traveling salesperson node(1..6). edge(1,(2;3;4)). edge(2,(4;5;6)). edge(3,(1;4;5)). edge(4,(1;2)). edge(5,(3;4;6)). edge(6,(2;3;5)). cost(1,2,2). cost(1,3,3). cost(1,4,1). cost(2,4,2). cost(2,5,2). cost(2,6,4). cost(3,1,3). cost(3,4,2). cost(3,5,2). cost(4,1,1). cost(4,2,2). cost(5,3,2). cost(5,4,2). cost(5,6,1). cost(6,2,4). cost(6,3,3). cost(6,5,1). edge(X,Y) :- cost(X,Y,_). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 102 / 541

  64. Case studies Traveling salesperson Traveling salesperson node(1..6). edge(1,(2;3;4)). edge(2,(4;5;6)). edge(3,(1;4;5)). edge(4,(1;2)). edge(5,(3;4;6)). edge(6,(2;3;5)). cost(1,2,2). cost(1,3,3). cost(1,4,1). cost(2,4,2). cost(2,5,2). cost(2,6,4). cost(3,1,3). cost(3,4,2). cost(3,5,2). cost(4,1,1). cost(4,2,2). cost(5,3,2). cost(5,4,2). cost(5,6,1). cost(6,2,4). cost(6,3,3). cost(6,5,1). edge(X,Y) :- cost(X,Y,_). node(X) :- cost(X,_,_). node(Y) :- cost(_,Y,_). Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 102 / 541

  65. Case studies Traveling salesperson Traveling salesperson { cycle(X,Y) : edge(X,Y) } = 1 :- node(X). { cycle(X,Y) : edge(X,Y) } = 1 :- node(Y). reached(Y) :- cycle(1,Y). reached(Y) :- cycle(X,Y), reached(X). :- node(Y), not reached(Y). #minimize { C,X,Y : cycle(X,Y), cost(X,Y,C) }. Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 103 / 541

  66. Case studies Traveling salesperson Traveling salesperson { cycle(X,Y) : edge(X,Y) } = 1 :- node(X). { cycle(X,Y) : edge(X,Y) } = 1 :- node(Y). reached(Y) :- cycle(1,Y). reached(Y) :- cycle(X,Y), reached(X). :- node(Y), not reached(Y). #minimize { C,X,Y : cycle(X,Y), cost(X,Y,C) }. Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 103 / 541

  67. Case studies Traveling salesperson Traveling salesperson { cycle(X,Y) : edge(X,Y) } = 1 :- node(X). { cycle(X,Y) : edge(X,Y) } = 1 :- node(Y). reached(Y) :- cycle(1,Y). reached(Y) :- cycle(X,Y), reached(X). :- node(Y), not reached(Y). #minimize { C,X,Y : cycle(X,Y), cost(X,Y,C) }. Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 103 / 541

  68. Case studies Traveling salesperson Traveling salesperson { cycle(X,Y) : edge(X,Y) } = 1 :- node(X). { cycle(X,Y) : edge(X,Y) } = 1 :- node(Y). reached(Y) :- cycle(1,Y). reached(Y) :- cycle(X,Y), reached(X). :- node(Y), not reached(Y). #minimize { C,X,Y : cycle(X,Y), cost(X,Y,C) }. Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 103 / 541

  69. Case studies Reviewer Assignment Outline 1 Elaboration tolerance 2 ASP solving process 3 Methodology 4 Case studies Satisfiability Queens Traveling salesperson Reviewer Assignment Planning Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 104 / 541

  70. Case studies Reviewer Assignment Reviewer Assignment Problem Instance A set of papers and a set of reviewers along with their first and second choices of papers and conflict of interests Problem Class A nice assignment of three reviewers to each paper Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 105 / 541

  71. Case studies Reviewer Assignment Reviewer Assignment Problem Instance A set of papers and a set of reviewers along with their first and second choices of papers and conflict of interests Problem Class A “nice” assignment of three reviewers to each paper Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 105 / 541

  72. Case studies Reviewer Assignment Reviewer Assignment by Ilkka Niemel¨ a paper(p1). reviewer(r1). classA(r1,p1). classB(r1,p2). coi(r1,p3). paper(p2). reviewer(r2). classA(r1,p3). classB(r1,p4). coi(r1,p6). [...] { assigned(P,R) : reviewer(R) } = 3 :- paper(P). :- assigned(P,R), coi(R,P). :- assigned(P,R), not classA(R,P), not classB(R,P). :- not 6 { assigned(P,R) : paper(P) } 9, reviewer(R). assignedB(P,R) :- classB(R,P), assigned(P,R). :- 3 { assignedB(P,R) : paper(P) }, reviewer(R). #minimize { 1,P,R : assignedB(P,R), paper(P), reviewer(R) }. Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 106 / 541

  73. Case studies Reviewer Assignment Reviewer Assignment by Ilkka Niemel¨ a paper(p1). reviewer(r1). classA(r1,p1). classB(r1,p2). coi(r1,p3). paper(p2). reviewer(r2). classA(r1,p3). classB(r1,p4). coi(r1,p6). [...] { assigned(P,R) : reviewer(R) } = 3 :- paper(P). :- assigned(P,R), coi(R,P). :- assigned(P,R), not classA(R,P), not classB(R,P). :- not 6 { assigned(P,R) : paper(P) } 9, reviewer(R). assignedB(P,R) :- classB(R,P), assigned(P,R). :- 3 { assignedB(P,R) : paper(P) }, reviewer(R). #minimize { 1,P,R : assignedB(P,R), paper(P), reviewer(R) }. Torsten Schaub (KRR@UP) Answer Set Solving in Practice October 20, 2018 106 / 541

Recommend

Integrating Problem Solving 2020 Integrating Problem Solving 2020 Integrating Problem Solving

Integrating Problem Solving 2020 Integrating Problem Solving 2020 Integrating Problem Solving

Integrating Problem Solving 2020 Integrating Problem Solving 2020 Integrating Problem Solving 2020 Integrating Problem Solving 2020 Integrating Problem Solving 2020 Integrating Problem Solving 2020 Integrating Problem Solving 2020 Integrating

738 views • 20 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.99k views • 195 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.84k views • 168 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.66k views • 161 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.27k views • 113 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.75k views • 132 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam Torsten Schaub (KRR@UP) ASP

Answer Set Solving in Practice Torsten Schaub University of Potsdam Torsten Schaub (KRR@UP) ASP

Answer Set Solving in Practice Torsten Schaub University of Potsdam Torsten Schaub (KRR@UP) ASP in Practice 1 / 69 Outline 1 Motivation 2 Introduction 3 Modeling by Example Graph Coloring Queens Traveling Salesperson 4 Meta Programming 5

1.92k views • 179 slides
Input. A set of men M , and a set of women W . Input. A set of men M , and a set of women W .

Input. A set of men M , and a set of women W . Input. A set of men M , and a set of women W .

Input. A set of men M , and a set of women W . Input. A set of men M , and a set of women W . Every agent has a set of acceptable partners. Input. A set of men M , and a set of women W . Every agent has a set of acceptable partners. The

1.12k views • 97 slides
Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin

Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin

Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin Gebser Torsten Schaub University of Potsdam Martin Gebser (University of Potsdam) Answer Set Programming 1 / 33 Outline 1 Motivation 2

1.37k views • 105 slides
Outline Motivation Answer Set Programming is a well-known declarative problem solving approach.

Outline Motivation Answer Set Programming is a well-known declarative problem solving approach.

Motivation Motivation Outline Motivation Answer Set Programming is a well-known declarative problem solving approach. Answer Set Programs with Queries over Subprograms 1 Motivation Christoph Redl The Saturation Technique and its

263 views • 10 slides
The Joy of Probabilistic Answer Set Programming Fabio G. Cozman Universidade de S ao Paulo

The Joy of Probabilistic Answer Set Programming Fabio G. Cozman Universidade de S ao Paulo

The Joy of Probabilistic Answer Set Programming Fabio G. Cozman Universidade de S ao Paulo Goal: to show that the credal semantics for Probabilistic Answer Set Programming (PASP) leads to a very useful modeling language. Answer set

376 views • 14 slides
Query Answering in (Resource-Based) answer set semantics Stefania Costantini and Andrea

Query Answering in (Resource-Based) answer set semantics Stefania Costantini and Andrea

Query Answering in (Resource-Based) answer set semantics Stefania Costantini and Andrea Formisano University of L Aquila and University of Perugia, Italy LRC15, Corunna, Spain Speaker: Stefania Answer Set Semantics The answer set

516 views • 23 slides
Answer Set Solving in Practice Martin Gebser and Torsten Schaub University of Potsdam

Answer Set Solving in Practice Martin Gebser and Torsten Schaub University of Potsdam

Answer Set Solving in Practice Martin Gebser and Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. M. Gebser and T. Schaub (KRR@UP)

1.47k views • 113 slides
Exam IV Results and Solu2ons High: 98 Low: 17 Average:

Exam IV Results and Solu2ons High: 98 Low: 17 Average:

Exam IV Results and Solu2ons High: 98 Low: 17 Average: 74 Answer: b Answer: c Answer: a Answer: c COOH Answer: c Answer: c

521 views • 35 slides
Answer Projection & Extraction NLP Systems and Applications Ling573 May 15, 2014 Roadmap

Answer Projection & Extraction NLP Systems and Applications Ling573 May 15, 2014 Roadmap

Answer Projection & Extraction NLP Systems and Applications Ling573 May 15, 2014 Roadmap Integrating Redundancy-based Answer Extraction Answer projection Answer reweighting Answer extraction as Sequence Tagging

435 views • 21 slides
Solving Systems Solving Systems by Graphing by Solving Systems by Substitution Graphing

Solving Systems Solving Systems by Graphing by Solving Systems by Substitution Graphing

Slide 1 / 176 Slide 2 / 176 Algebra I System of Linear Equations 2015-11-02 www.njctl.org Slide 3 / 176 Slide 4 / 176 Table of Contents Click on the topic to go to that section Solving Systems Solving Systems by Graphing by Solving

599 views • 30 slides
CEE 772: Instrumental Methods in Environmental Analysis Lecture #19 Mass Spectrometry: Basics

CEE 772: Instrumental Methods in Environmental Analysis Lecture #19 Mass Spectrometry: Basics

Updated: 11 November 2014 Print version CEE 772: Instrumental Methods in Environmental Analysis Lecture #19 Mass Spectrometry: Basics (Skoog, Chapt. 11, 26, 27, 28, pp.253-271, 674-693 718-721, 738-739 ) (Harris, Chapt. 23, 24 & 25)

748 views • 42 slides
L. Li (LMD/CNRS): Three cells page 1 Zonally-averaged transport equation For a whatever scalar

L. Li (LMD/CNRS): Three cells page 1 Zonally-averaged transport equation For a whatever scalar

L. Li (LMD/CNRS): Three cells page 1 Zonally-averaged transport equation For a whatever scalar variable Q , the transport equation (with pres- sure as vertical coordinate) can be written as: Q t + uQ x + v Q y + Q p =

428 views • 14 slides
how do multiple planetary systems shape the dust disk? . introduction . We are now

how do multiple planetary systems shape the dust disk? . introduction . We are now

The HL Tau system . Giovanni Picogna Tbingen Universitt, CPT & Kepler Center 6th May 2015 Exoplanets in Lund 2015 Lund Observatory how do multiple planetary systems shape the dust disk? . introduction . We are now obtaining

791 views • 58 slides
CLLJ and WHWP heat content as a constrain to North American Monsoon activation moisture supply A.

CLLJ and WHWP heat content as a constrain to North American Monsoon activation moisture supply A.

CLLJ and WHWP heat content as a constrain to North American Monsoon activation moisture supply A. M Durn-Quesada , R. Castillo , M. Hundsdoerfer and L. Gimeno CHyCle-2017 Fig 1. Climatological monthly mean of precipitation based on CMAP data

301 views • 12 slides
Exploring Gluonic Matter with Electron-Ion Collisions Outline Gluon, Saturation

Exploring Gluonic Matter with Electron-Ion Collisions Outline Gluon, Saturation

Exploring Gluonic Matter with Electron-Ion Collisions Outline Gluon, Saturation Electron-Ion Collider Signals of saturation/Selected key measurements in eA J.H. Lee Brookhaven National Laboratory QM2012, Washington D.C. 1

582 views • 20 slides
After the discovery of a Higgs boson(-like) particle a theorists perspective Heidi

After the discovery of a Higgs boson(-like) particle a theorists perspective Heidi

After the discovery of a Higgs boson(-like) particle a theorists perspective Heidi Rzehak Albert-Ludwigs-Universit at Freiburg February 21, 2014 Discoveries at the LHC Expectations (2008): t Hooft: Gross: Veltman: A

630 views • 42 slides
Normal Shock Waves Lecture 24 ME EN 412 Andrew Ning aning@byu.edu Outline Normal Shock Waves

Normal Shock Waves Lecture 24 ME EN 412 Andrew Ning aning@byu.edu Outline Normal Shock Waves

Normal Shock Waves Lecture 24 ME EN 412 Andrew Ning aning@byu.edu Outline Normal Shock Waves Example Normal Shock Waves Normal Shock Waves 1 2 Prandtl relation u 1 u 2 = a 2 = 2 + ( 1) M 2 u 2 = 1 1 ( + 1) M 2 u 1 2

256 views • 7 slides
Oblique Shock and Expansion Waves Lecture 27-28 ME EN 412 Andrew Ning aning@byu.edu Outline

Oblique Shock and Expansion Waves Lecture 27-28 ME EN 412 Andrew Ning aning@byu.edu Outline

Oblique Shock and Expansion Waves Lecture 27-28 ME EN 412 Andrew Ning aning@byu.edu Outline Oblique Shock Waves Expansion Waves Applications Oblique Shock Waves NASA, Public Domain V 1 n V 1 t V 2 V 1 V 2 t V 2 n M > 1

207 views • 9 slides

More recommend

Explore More Topics

Stay informed with curated content and fresh updates.

animals pets art culture automotive transportation business finance computer internet construction architecture education-career electronics communication

Logo Sambuz

Unleash a World of Digital Possibilities—Browse, Share, and Explore Content Without Boundaries

Useful Links

About Us Privacy Services FAQ's Contact

Newsletter

Stay Informed & Inspired—Subscribe for the Latest Updates, Tips, and Exclusive Content Directly to Your Inbox.

Mail Us

mail@sambuz.com

2026 SAMBUZ, All right reserved.