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- 1. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References A Survey of Evaluation Techniques and Systems for Answer Set Programming Francesco Ricca University of Calabria, Italy Klagenfurt 2019 Francesco Ricca Techniques and Systems for ASP
- 2. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Outline 1 Introduction and Preliminaries 2 Evaluation Techniques and Systems 3 Interfaces and Systems for Extensions Francesco Ricca Techniques and Systems for ASP
- 3. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Answer Set Programming (ASP) (1) Answer Set Programming (ASP)[BET11] Declarative programming paradigm Non-monotonic reasoning and logic programming Stable model semantics [GL91] Expressive KRR Language Roots in Datalog and Nonmonotonic logic Extended over the years to ease modeling → Disjunction, (Weak) Constraints, Aggregates, Functions... Can model problems up to ΣP 2 /ΠP 2 [EGM97, DEGV01] → even problems not (polynomially) translatable to SAT Standardized syntax: ASPCore 2.0 [CFG+ 12] Francesco Ricca Techniques and Systems for ASP
- 4. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Answer Set Programming (ASP) (2) Idea: 1 Represent a computational problem by a Logic program 2 Answer sets correspond to problem solutions 3 Use an ASP solver to ﬁnd these solutions Francesco Ricca Techniques and Systems for ASP
- 5. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Answer Set Programming (ASP) (3) ASP: A Major paradigm for logic-based AI 1 Declarative, readable and expressive language → stable model semantics, language extensions [GL91]) 2 Robust and efﬁcient implementations [LMR16] → continuous improvements (see ASP comp. [CGMR16, GMR17]) 3 Applications in several ﬁelds [EGL16] Workforce Management, Planning, Scheduling, Information Integration, Data cleaning, Bioinformatics, Robotics, Natural Language Understanding, ... see e.g. [Lif02, EFLP99, EFLP99, EIST06, EEB10, Sak11, SN99, DGH09, CHO+ 09, RDG+ 10, RGA+ 12, GNA13] Francesco Ricca Techniques and Systems for ASP
- 6. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Answer Set Programming (ASP) (3) ASP: A Major paradigm for logic-based AI 1 Declarative, readable and expressive language → stable model semantics, language extensions [GL91]) 2 Robust and efﬁcient implementations [LMR16] → continuous improvements (see ASP comp. [CGMR16, GMR17]) 3 Applications in several ﬁelds [EGL16] Workforce Management, Planning, Scheduling, Information Integration, Data cleaning, Bioinformatics, Robotics, Natural Language Understanding, ... see e.g. [Lif02, EFLP99, EFLP99, EIST06, EEB10, Sak11, SN99, DGH09, CHO+ 09, RDG+ 10, RGA+ 12, GNA13] Francesco Ricca Techniques and Systems for ASP
- 7. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Answer Set Programming (ASP) (3) ASP: A Major paradigm for logic-based AI 1 Declarative, readable and expressive language → stable model semantics, language extensions [GL91]) 2 Robust and efﬁcient implementations [LMR16] → continuous improvements (see ASP comp. [CGMR16, GMR17]) 3 Applications in several ﬁelds [EGL16] Workforce Management, Planning, Scheduling, Information Integration, Data cleaning, Bioinformatics, Robotics, Natural Language Understanding, ... see e.g. [Lif02, EFLP99, EFLP99, EIST06, EEB10, Sak11, SN99, DGH09, CHO+ 09, RDG+ 10, RGA+ 12, GNA13] Francesco Ricca Techniques and Systems for ASP
- 8. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Answer Set Programming (ASP) (3) ASP: A Major paradigm for logic-based AI 1 Declarative, readable and expressive language → stable model semantics, language extensions [GL91]) 2 Robust and efﬁcient implementations [LMR16] → continuous improvements (see ASP comp. [CGMR16, GMR17]) 3 Applications in several ﬁelds [EGL16] Workforce Management, Planning, Scheduling, Information Integration, Data cleaning, Bioinformatics, Robotics, Natural Language Understanding, ... see e.g. [Lif02, EFLP99, EFLP99, EIST06, EEB10, Sak11, SN99, DGH09, CHO+ 09, RDG+ 10, RGA+ 12, GNA13] Francesco Ricca Techniques and Systems for ASP
- 9. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References ASP Syntax Rule: a1 | . . . | an :- b1, . . . , bk , not bk+1, . . . , not bm. head body Atoms and Literals: ai , bi , not bi Positive Body: b1, . . . , bk Negative Body: not bk+1, . . . , not bm. Fact: A rule with empty body Constraint: A rule with empty head Variables: allowed in atom’s arguments Must occur in the positive body (Safety) Can be seen as placeholders for constants Francesco Ricca Techniques and Systems for ASP
- 10. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References ASP Syntax Rule: a1 | . . . | an :- b1, . . . , bk , not bk+1, . . . , not bm. head body Atoms and Literals: ai , bi , not bi Positive Body: b1, . . . , bk Negative Body: not bk+1, . . . , not bm. Fact: A rule with empty body Constraint: A rule with empty head Variables: allowed in atom’s arguments Must occur in the positive body (Safety) Can be seen as placeholders for constants Francesco Ricca Techniques and Systems for ASP
- 11. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Informal Semantics Rule: a1 | . . . | an :- b1, . . . , bk , not bk+1, . . . , not bm. head body Informal Semantics: “If all b1, . . . , bk are true and all bk+1, . . . , bm are not true, then at least one among a1, . . . , an is true”. Francesco Ricca Techniques and Systems for ASP
- 12. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Informal Semantics Rule: a1 | . . . | an :- b1, . . . , bk , not bk+1, . . . , not bm. head body Informal Semantics: “If all b1, . . . , bk are true and all bk+1, . . . , bm are not true, then at least one among a1, . . . , an is true”. Example isInterestedinASP(X) | isCurious(X) :- attendsASP(X). attendsASP(john). Two (minimal) models encoding two plausible scenarios: M1:{isInterestedinASP(john), attendsASP(john).} M2:{isCurious(john), attendsASP(john).} Francesco Ricca Techniques and Systems for ASP
- 13. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Informal Semantics (3) Constraint: :- b1, . . . , bk , not bk+1, . . . , not bm. Informal Semantics: “It is not possible that all b1, . . . , bk are true and all bk+1, . . . , bm are false”. Example isInterestedinASP(X) | isCurious(X) :- attendsASP(X). :- hatesASP(X), isInterestedinASP(X). attendsASP(john). hatesASP(john). Only one plausible scenario: M1:{isInterestedinASP(john), attendsASP(john), hatesASP(john).} M2:{isCurious(john), attendsASP(john), hatesASP(john).} Francesco Ricca Techniques and Systems for ASP
- 14. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Informal Semantics (3) Constraint: :- b1, . . . , bk , not bk+1, . . . , not bm. Informal Semantics: “It is not possible that all b1, . . . , bk are true and all bk+1, . . . , bm are false”. Example isInterestedinASP(X) | isCurious(X) :- attendsASP(X). :- hatesASP(X), isInterestedinASP(X). attendsASP(john). hatesASP(john). Only one plausible scenario: M1:{isInterestedinASP(john), attendsASP(john), hatesASP(john).} M2:{isCurious(john), attendsASP(john), hatesASP(john).} Francesco Ricca Techniques and Systems for ASP
- 15. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Extensions for Modeling Optimization Problems Weak Constraints: Express desiderata Constraints which should possibly be satisﬁed (as soft constraints in CSP) Syntax: :∼ b(X, Y). Intuitive meaning: “set b as false, if possible” Francesco Ricca Techniques and Systems for ASP
- 16. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Extensions for Modeling Optimization Problems Weak Constraints: Express desiderata Constraints which should possibly be satisﬁed (as soft constraints in CSP) Syntax: :∼ b(X, Y). [w@p] Weigth and Priority: ([w@p]) • higher weights/priorities ⇒ higher importance • “@p” can be omitted “minimize the sum of the weights of the violated constraints in the highest priority level, and so on” Declarative speciﬁcation of optimization problems Francesco Ricca Techniques and Systems for ASP
- 17. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Aggregates (Informal) Aggregate atoms: Express functions calculated over sets of elements: Lg <op f{S} <op Ug Example 5 < #count{EmpId : emp(EmpId, male, Skill, Salary)} ≤ 10 The atom is true if the number of male employees is greater than 5 and does not exceed 10. Francesco Ricca Techniques and Systems for ASP
- 18. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Aggregates (Informal) Aggregate atoms: Express functions calculated over sets of elements: Lg <op f{S} <op Ug Example 5 < #count{EmpId : emp(EmpId, male, Skill, Salary)} ≤ 10 The atom is true if the number of male employees is greater than 5 and does not exceed 10. Allows for compact speciﬁcations of rules and constraints! Francesco Ricca Techniques and Systems for ASP
- 19. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Programming in ASP (Example 1) Example (3-col) Problem: Given a graph, assign one color out of 3 colors to each node such that two adjacent nodes have always different colors. Input: a Graph is represented by node(_) and edge(_, _). % guess a coloring for the nodes (r) col(X, red) | col(X, yellow) | col(X, green) :- node(X). % discard colorings where adjacent nodes have the same color (c) :- edge(X, Y), col(X, C), col(Y, C). % NB: answer sets are subset minimal → only one color per node Francesco Ricca Techniques and Systems for ASP
- 20. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Programming in ASP (Example 1) Example (3-col) Problem: Given a graph, assign one color out of 3 colors to each node such that two adjacent nodes have always different colors. Input: a Graph is represented by node(_) and edge(_, _). % guess a coloring for the nodes (r) col(X, red) | col(X, yellow) | col(X, green) :- node(X). % discard colorings where adjacent nodes have the same color (c) :- edge(X, Y), col(X, C), col(Y, C). % NB: answer sets are subset minimal → only one color per node Francesco Ricca Techniques and Systems for ASP
- 21. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Programming in ASP (Example 1) Example (3-col) Problem: Given a graph, assign one color out of 3 colors to each node such that two adjacent nodes have always different colors. Input: a Graph is represented by node(_) and edge(_, _). % guess a coloring for the nodes (r) col(X, red) | col(X, yellow) | col(X, green) :- node(X). % discard colorings where adjacent nodes have the same color (c) :- edge(X, Y), col(X, C), col(Y, C). % NB: answer sets are subset minimal → only one color per node Francesco Ricca Techniques and Systems for ASP
- 22. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Programming in ASP (Example 1) Example (3-col) Problem: Given a graph, assign one color out of 3 colors to each node such that two adjacent nodes have always different colors. Input: a Graph is represented by node(_) and edge(_, _). % guess a coloring for the nodes (r) col(X, red) | col(X, yellow) | col(X, green) :- node(X). % discard colorings where adjacent nodes have the same color (c) :- edge(X, Y), col(X, C), col(Y, C). % NB: answer sets are subset minimal → only one color per node Francesco Ricca Techniques and Systems for ASP
- 23. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Programming in ASP (Example 2) Example (Team Building) % An employee is either included in the team or not inTeam(I) | outTeam(I) :- emp(I, Sx, Sk, Sa). % The team consists of a certain number of employees :- nEmp(N), #count{I : inTeam(I)} <> N. % At least a given number of different skills must be present in the team :- nSkill(M), #count{Sk : emp(I, Sx, Sk, Sa), inTeam(I)} < M. % The sum of the salaries of the employees working in the team must not exceed the given budget :- budget(B), #sum{Sa, I : emp(I, Sx, Sk, Sa), inTeam(I)} > B. % The salary of each individual employee is within a speciﬁed limit :- maxSal(M), #max{Sa : emp(I, Sx, Sk, Sa), inTeam(I)} > M. Francesco Ricca Techniques and Systems for ASP
- 24. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Programming in ASP (Example 3) Example (Traveling Salesman Person) Problem: Find a path of minimum length in a Weighted Graph beginning at the starting node which contains all nodes of the graph. Input: node(_) and edge(_, _, _), and start(_). % Guess a path inPath(X, Y) | outPath(X, Y) :- edge(X, Y, _). % Ensure that it is Hamiltonian :- #count{X : inPath(X, Y)} > 1. :- #count{Y : inPath(X, Y)} > 1. :- node(X), not reached(X). :- inPath(X, Y), start(Y). reached(X) :- reached(Y), inPath(Y, X). reached(X) :- start(X). % Minimize the sum of distances :∼ inPath(X, Y), edge(X, Y, C). [C] | Guess | | Check | | | Aux. Rules | | Optimize Francesco Ricca Techniques and Systems for ASP
- 25. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Programming in ASP (Example 3) Example (Traveling Salesman Person) Problem: Find a path of minimum length in a Weighted Graph beginning at the starting node which contains all nodes of the graph. Input: node(_) and edge(_, _, _), and start(_). % Guess a path inPath(X, Y) | outPath(X, Y) :- edge(X, Y, _). % Ensure that it is Hamiltonian :- #count{X : inPath(X, Y)} > 1. :- #count{Y : inPath(X, Y)} > 1. :- node(X), not reached(X). :- inPath(X, Y), start(Y). reached(X) :- reached(Y), inPath(Y, X). reached(X) :- start(X). % Minimize the sum of distances :∼ inPath(X, Y), edge(X, Y, C). [C] | Guess | | Check | | | Aux. Rules | | Optimize Francesco Ricca Techniques and Systems for ASP
- 26. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Programming in ASP (Example 3) Example (Traveling Salesman Person) Problem: Find a path of minimum length in a Weighted Graph beginning at the starting node which contains all nodes of the graph. Input: node(_) and edge(_, _, _), and start(_). % Guess a path inPath(X, Y) | outPath(X, Y) :- edge(X, Y, _). % Ensure that it is Hamiltonian :- #count{X : inPath(X, Y)} > 1. :- #count{Y : inPath(X, Y)} > 1. :- node(X), not reached(X). :- inPath(X, Y), start(Y). reached(X) :- reached(Y), inPath(Y, X). reached(X) :- start(X). % Minimize the sum of distances :∼ inPath(X, Y), edge(X, Y, C). [C] | Guess | | Check | | | Aux. Rules | | Optimize Francesco Ricca Techniques and Systems for ASP
- 27. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Main Evaluation Strategies Evaluation of ASP Programs [KLPS16] Traditionally a two-step process: “Ground+Solve” 1 Instantiation or grounding → Variable elimination → Exponential output → Support language features & Keep output small!! 2 Propositional search or ASP solving → Model Generation: “compute models” → related to SAT → (Stable) Model Checking: “check if model is stable” → coNP Single step evaluation: “Grounding-less” → Grounding bottleneck → Grounding and search interleaved Francesco Ricca Techniques and Systems for ASP
- 28. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References The traditional Architecture of ASP Systems “Pay as you go approach” The instantiator can often evaluate stratiﬁed programs The model generator or solver sufﬁces for normal/HCF The model checker needed for unrestricted disjunction Francesco Ricca Techniques and Systems for ASP
- 29. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References About the Instantiation Some facts: Exponential in the worst case Input of a subsequent exponential procedure Signiﬁcantly affects the performance of the overall process Full instantiation: i.e., apply every possible substitution → Not viable in practice Intelligent instantiation → Keep the size of the instantiation as small as possible → Equivalent to the full one → Intelligent Instantiators can solve problems in P → Deductive Databases as a subcase! Francesco Ricca Techniques and Systems for ASP
- 30. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References About the Instantiation Some facts: Exponential in the worst case Input of a subsequent exponential procedure Signiﬁcantly affects the performance of the overall process Full instantiation: i.e., apply every possible substitution → Not viable in practice Intelligent instantiation → Keep the size of the instantiation as small as possible → Equivalent to the full one → Intelligent Instantiators can solve problems in P → Deductive Databases as a subcase! Francesco Ricca Techniques and Systems for ASP
- 31. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References About the Instantiation Some facts: Exponential in the worst case Input of a subsequent exponential procedure Signiﬁcantly affects the performance of the overall process Full instantiation: i.e., apply every possible substitution → Not viable in practice Intelligent instantiation → Keep the size of the instantiation as small as possible → Equivalent to the full one → Intelligent Instantiators can solve problems in P → Deductive Databases as a subcase! Francesco Ricca Techniques and Systems for ASP
- 32. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Instantiation Example: 3-Colorability % guess a coloring for the nodes (r) col(X, red) | col(X, yellow) | col(X, green) :- node(X). % discard colorings where adjacent nodes have the same color (c) :- edge(X, Y), col(X, C), col(Y, C). Instance: node(1). node(2). node(3). edge(1, 2). edge(2, 3). Francesco Ricca Techniques and Systems for ASP
- 33. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Instantiation Example: 3-Colorability % guess a coloring for the nodes (r) col(X, red) | col(X, yellow) | col(X, green) :- node(X). % discard colorings where adjacent nodes have the same color (c) :- edge(X, Y), col(X, C), col(Y, C). Instance: node(1). node(2). node(3). edge(1, 2). edge(2, 3). Full Theoretical Instantiation: col(red, red) | col(red, yellow) | col(red, green) :- node(red). col(yellow, red) | col(yellow, yellow) | col(yellow, green) :- node(yellow). col(green, red) | col(green, yellow) | col(green, green) :- node(green). . . . col(1, red) | col(1, yellow) | col(1, green) :- node(1). . . . :- edge(1, 2), col(1, 1), col(2, 1). . . . :- edge(1, 2), col(1, red), col(2, red). . . . Francesco Ricca Techniques and Systems for ASP
- 34. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Instantiation Example: 3-Colorability % guess a coloring for the nodes (r) col(X, red) | col(X, yellow) | col(X, green) :- node(X). % discard colorings where adjacent nodes have the same color (c) :- edge(X, Y), col(X, C), col(Y, C). Instance: node(1). node(2). node(3). edge(1, 2). edge(2, 3). Full Theoretical Instantiation: → is huge (2916 rules) and redundant! col(red, red) | col(red, yellow) | col(red, green) :- node(red). col(yellow, red) | col(yellow, yellow) | col(yellow, green) :- node(yellow). col(green, red) | col(green, yellow) | col(green, green) :- node(green). . . . col(1, red) | col(1, yellow) | col(1, green) :- node(1). ← OK! . . . :- edge(1, 2), col(1, 1), col(2, 1). ← redundant! . . . :- edge(1, 2), col(1, red), col(2, red). ← OK! . . . Francesco Ricca Techniques and Systems for ASP
- 35. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Instantiation Example: 3-Colorability % guess a coloring for the nodes (r) col(X, red) | col(X, yellow) | col(X, green) :- node(X). % discard colorings where adjacent nodes have the same color (c) :- edge(X, Y), col(X, C), col(Y, C). Instance: node(1). node(2). node(3). edge(1, 2). edge(2, 3). Intelligent Instantiation: → equivalent but much smaller (9 rules)! col(1, red) | col(1, yellow) | col(1, green). col(2, red) | col(2, yellow) | col(2, green). col(3, red) | col(3, yellow) | col(3, green). :- col(1, red), col(2, red). :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). Francesco Ricca Techniques and Systems for ASP
- 36. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation & Checking Model Generator or Solver → produces candidate models Works on propositional programs Similar to a SAT solver Intelligent backtracking algorithm Propagate Deterministic Consequences → Unit Propagation, Support Propagation, → Well-founded Negation, etc. Assume a literal l (heuristically) until a model is generated Upon inconsistency Backtrack (assume not l) Model Checker → checks if candidates are Answer Sets Enabled only for hard (non-HCF) instances Implements a coNP-complete task Francesco Ricca Techniques and Systems for ASP
- 37. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation & Checking Model Generator or Solver → produces candidate models Works on propositional programs Similar to a SAT solver Intelligent backtracking algorithm Propagate Deterministic Consequences → Unit Propagation, Support Propagation, → Well-founded Negation, etc. Assume a literal l (heuristically) until a model is generated Upon inconsistency Backtrack (assume not l) Model Checker → checks if candidates are Answer Sets Enabled only for hard (non-HCF) instances Implements a coNP-complete task Francesco Ricca Techniques and Systems for ASP
- 38. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation Example: 3-Colorability Model Generation step: col(1, red) | col(1, yellow) | col(1, green). col(2, red) | col(2, yellow) | col(2, green). col(3, red) | col(3, yellow) | col(3, green). :- col(1, red), col(2, red). :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). True: {} False: {} Francesco Ricca Techniques and Systems for ASP
- 39. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation Example: 3-Colorability Model Generation step: Chose literal col(1, red) | col(1, yellow) | col(1, green). col(2, red) | col(2, yellow) | col(2, green). col(3, red) | col(3, yellow) | col(3, green). :- col(1, red), col(2, red). :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). True: {} ← col(1, red) False: {} Francesco Ricca Techniques and Systems for ASP
- 40. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation Example: 3-Colorability Model Generation step: Propagate Deterministic Consequences col(1, red) | col(1, yellow) | col(1, green). ← 1-support propagation col(2, red) | col(2, yellow) | col(2, green). col(3, red) | col(3, yellow) | col(3, green). :- col(1, red), col(2, red). ← 2-unit propagation :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). True: {col(1, red)} False: { col(1, yellow), col(1, green), col(2, red) } Francesco Ricca Techniques and Systems for ASP
- 41. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation Example: 3-Colorability Model Generation step: Chose literal col(1, red) | col(1, yellow) | col(1, green). col(2, red) | col(2, yellow) | col(2, green). col(3, red) | col(3, yellow) | col(3, green). :- col(1, red), col(2, red). :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). True: {col(1, red) ← col(2, yellow) } False: { col(1, yellow), col(1, green), col(2, red) } Francesco Ricca Techniques and Systems for ASP
- 42. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation Example: 3-Colorability Model Generation step: Propagate Deterministic Consequences col(1, red) | col(1, yellow) | col(1, green). col(2, red) | col(2, yellow) | col(2, green). ←1-support propagation col(3, red) | col(3, yellow) | col(3, green). :- col(1, red), col(2, red). :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). ← 2-unit propagation True: {col(1, red), col(2, yellow) } False: { col(1, yellow), col(1, green), col(2, red), col(2, green), col(3, yellow) } Francesco Ricca Techniques and Systems for ASP
- 43. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation Example: 3-Colorability Model Generation step: Chose literal col(1, red) | col(1, yellow) | col(1, green). col(2, red) | col(2, yellow) | col(2, green). col(3, red) | col(3, yellow) | col(3, green). :- col(1, red), col(2, red). :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). True: {col(1, red), col(2, yellow)} ← col(3, red) False: { col(1, yellow), col(1, green), col(2, red), col(2, green), col(3, yellow) } Francesco Ricca Techniques and Systems for ASP
- 44. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation Example: 3-Colorability Model Generation step: Propagate Deterministic Consequences col(1, red) | col(1, yellow) | col(1, green). col(2, red) | col(2, yellow) | col(2, green). col(3, red) | col(3, yellow) | col(3, green). ←support propagation :- col(1, red), col(2, red). :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). True: {col(1, red), col(2, yellow), col(3, red) False: { col(1, yellow), col(1, green), col(2, red), col(2, green), col(3, yellow) col(3, green) } Francesco Ricca Techniques and Systems for ASP
- 45. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Generation Example: 3-Colorability Model Generation step: Answer set found! col(1, red) | col(1, yellow) | col(1, green). col(2, red) | col(2, yellow) | col(2, green). col(3, red) | col(3, yellow) | col(3, green). :- col(1, red), col(2, red). :- col(1, green), col(2, green). :- col(1, yellow), col(2, yellow). :- col(2, red), col(3, red). :- col(2, green), col(3, green). :- col(2, yellow), col(3, yellow). Answer Set: {col(1, red), col(2, yellow), col(3, red) } Francesco Ricca Techniques and Systems for ASP
- 46. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (1) Consider: M = {a, b} a | b | c. a :- b. b :- a, not c.. a :- c. Francesco Ricca Techniques and Systems for ASP
- 47. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (1) Step:(1) Consider: M = {a, b} a | b | c. a :- b. b :- a, not c.. a :- c. Francesco Ricca Techniques and Systems for ASP
- 48. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (1) Step:(2) Consider: M = {a, b} a | b | c. a :- b. b :- a, not c. Francesco Ricca Techniques and Systems for ASP
- 49. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (1) Step:(3) Consider: M = {a, b} a | b | c. a :- b. b :- a. Francesco Ricca Techniques and Systems for ASP
- 50. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (2) Consider: M = {a, b} a | b. a :- b. b :- a. Francesco Ricca Techniques and Systems for ASP
- 51. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (2) Step: (6-9) Consider: M = {a, b} a | b. =⇒ ← a ∧ b a :- b. b :- a. Francesco Ricca Techniques and Systems for ASP
- 52. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (2) Step: (6-9) Consider: M = {a, b} a | b. =⇒ ← a ∧ b a :- b. =⇒ b ← a b :- a. Francesco Ricca Techniques and Systems for ASP
- 53. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (2) Step: (6-9) Consider: M = {a, b} a | b. =⇒ ← a ∧ b a :- b. =⇒ b ← a b :- a. =⇒ a ← b Francesco Ricca Techniques and Systems for ASP
- 54. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (2) Step: (6-9) Consider: M = {a, b} =⇒ a ∨ b ← a | b. =⇒ ← a ∧ b a :- b. =⇒ b ← a b :- a. =⇒ a ← b Francesco Ricca Techniques and Systems for ASP
- 55. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (2) Step: (6-9) Consider: M = {a, b} =⇒ a ∨ b a | b. =⇒ ← a ∧ b =⇒ ¬a ∨ ¬b a :- b. =⇒ b ← a =⇒ ¬a ∨ b b :- a. =⇒ a ← b =⇒ ¬b ∨ a Francesco Ricca Techniques and Systems for ASP
- 56. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Model Checking via SAT test (2) Consider: M = {a, b} =⇒ a ∨ b =⇒ ¬a ∨ ¬b =⇒ ¬a ∨ b =⇒ ¬b ∨ a Unsatisﬁable → Answer Set! Francesco Ricca Techniques and Systems for ASP
- 57. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Evolution of grounders Lparse [SN01] → front-end system → intermediate format → normal programs → ω-restricted → “domains” DLV [LPF+ 06] → disjunctive programs → safety condition → deductive database techniques Gringo [GST07] → front-end system → Lparse format → λ-restricted → “positive recursion” Gringo v.3+ and i-dlv [GKKS11, CFPZ17] → Reinterpret DLV’s + new tech. (e.g., decompositions [BMMW17]) → ASPCore2 standard language + Language extensions Francesco Ricca Techniques and Systems for ASP
- 58. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Evolution of grounders Lparse [SN01] → front-end system → intermediate format → normal programs → ω-restricted → “domains” DLV [LPF+ 06] → disjunctive programs → safety condition → deductive database techniques Gringo [GST07] → front-end system → Lparse format → λ-restricted → “positive recursion” Gringo v.3+ and i-dlv [GKKS11, CFPZ17] → Reinterpret DLV’s + new tech. (e.g., decompositions [BMMW17]) → ASPCore2 standard language + Language extensions Francesco Ricca Techniques and Systems for ASP
- 59. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Native Solvers & Systems DPLL-based [DLL62] Smodels [SNS02] → dedicated inferences normal programs GnT [JNS+ 06] → disj. model checking based on Smodels DLV [LPF+ 06] → disj. unfounded sets + SAT-based check [? ] CDCL-based [SLM09] Clasp [GKNS07] → nogood learning + SAT tech. Wasp [ADLR15] → clause learning + SAT tech. Beyond CDCL (and ASP) Clingo [GKK+ 16] → monolithic (Gringo + Clasp) + ... DLV 2.0 [ACD+ 17] → monolithic (i-dlv + Wasp) + ... Francesco Ricca Techniques and Systems for ASP
- 60. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Translation-based solvers Translation to SAT Cmodels (v1) → Clark completion for tight programs [EL03] assat [LZ02] & Cmodels (v2) [LM04] → Loop formulas Cmodels (v3) [GLM06] → disj. via SAT-based stability check lp2sat [Jan06, JN11] → level rankings [Nie08] Other target formalisms lp2acyc [GJR] → aciclycity condition lp2mip [LJN12] → mixed integer programming lp2* [JNS09, NJN11] → PB-Constraint, Diff. Logic, Bit Vector Francesco Ricca Techniques and Systems for ASP
- 61. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Grounding less systems Lazy grounding (Interleave/blend grounding+search) GASP [PDPR09] → Based on [LPST10] ASPERIX [LN09] → Based on [LPST10] OMIGA [DEF+ 12] → Based on Rete [For82] ALPHA [Wei17] → Lazy grounding + CDCL IDP [dCDBS15] → Lazy model expansion Francesco Ricca Techniques and Systems for ASP
- 62. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Multiprocessing & Portfolios Portfolio systems (Dominating ASP Competitions since 2011) Claspfolio [GKK+ 11a, HLS14] → SATZILLA approach [XHHL08] ME-ASP [MPR14, MPR15] → AQME approach [PT09] ASPEED & PPfolio → Optimized portfolios [HKLS15] Multiprocessing DLV parallel grounding [PRS13] (SMP machines) Lparse + DPLL-based parallel ASP solvers → [FMMT01, PBB03, BPEL05, GJM+ 06] based on [ZBH96] Multiprocessing variants of Clasp [GKK+ 11b, GKS12, GKK+ 15] → Parallel & distributed CDCL-search & portfolio ASP solving utilizing GPUs [DFPV16] Francesco Ricca Techniques and Systems for ASP
- 63. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Systems Interfaces ASP Systems Highly optimized and sophisticated implementations Extensions are non-obvious API to make extensions easier Clingo API [GKK+b] → Customized solving control via C, lua and python scripts → Incremental solving [GKK+ a] and External propagators [DW12] Wasp API [ADLR15] → Solver extension via Python, C++, and Perl → Domain Heuristics [DGL+ 16] and Custom Propagators [CDRS17] DLV 2.0 [ACD+ 17] → i-dlv + Wasp easier development of propagators. Francesco Ricca Techniques and Systems for ASP
- 64. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Systems Interfaces ASP Systems Highly optimized and sophisticated implementations Extensions are non-obvious API to make extensions easier Clingo API [GKK+b] → Customized solving control via C, lua and python scripts → Incremental solving [GKK+ a] and External propagators [DW12] Wasp API [ADLR15] → Solver extension via Python, C++, and Perl → Domain Heuristics [DGL+ 16] and Custom Propagators [CDRS17] DLV 2.0 [ACD+ 17] → i-dlv + Wasp easier development of propagators. Francesco Ricca Techniques and Systems for ASP
- 65. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Systems for ASP Extensions Advanced frameworks based on ASP Constraint ASP (CASP) [BBG05, BKOS17, BL17] → Augment the Boolean representations of ASP with constraints → Systems: ACSOLVER, CLINGCON, EZCSP, IDP, INCA, and MINGO ASP Modulo Theories (ASPMT) [SL16] → Systems: ASPMT2SMT, EZSMT Bound-Founded ASP (BFASP) [ACS13] → System: CHUFFED (CP solver + propagator BF integer variables) Higher-order EXternal (HEX) programs [EFI+16] → ASP programs + external sources (e.g., ontological reasoning) → System: DLVHEX Francesco Ricca Techniques and Systems for ASP
- 66. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Conclusion 1 History of ASP Implementations Ground + Solve → Grounders, Native and Translation-based Solvers → Portfolios and Parallel-distributed implementations Grounding-less 2 Interfaces and Extensions Easy extensions with Python, C++, etc. → Customized control over grounding and solving → New Heuristics and Propagators 3 Systems for ASP Extensions Constraint ASP (CASP), ASPMT, HEX Programs, etc. Francesco Ricca Techniques and Systems for ASP
- 67. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Acknowledgments Thanks for your attention! Francesco Ricca Techniques and Systems for ASP
- 68. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References Thanks to my co-authors All the details and references in our paper: [GLMPRS18] Martin Gebser, Nicola Leone, Marco Maratea, Simona Perri, Francesco Ricca, Torsten Schaub: “Evaluation Techniques and Systems for Answer Set Programming: a Survey” Proceedings of IJCAI 2018, pg. 5450-5456 AAAI Press Francesco Ricca Techniques and Systems for ASP
- 69. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References [ACD+ 17] Mario Alviano, Francesco Calimeri, Carmine Dodaro, Davide Fuscà, Nicola Leone, Simona Perri, Francesco Ricca, Pierfrancesco Veltri, and Jessica Zangari. The ASP system DLV2. In LPNMR, volume 10377 of Lecture Notes in Computer Science, pages 215–221. Springer, 2017. [ACS13] R. A. Aziz, G. Chu, and P. J. Stuckey. Stable model semantics for founded bounds. TPLP, 13(4-5):517–532, 2013. [ADLR15] Mario Alviano, Carmine Dodaro, Nicola Leone, and Francesco Ricca. Advances in WASP. In LPNMR, volume 9345 of Lecture Notes in Computer Science, pages 40–54. Springer, 2015. [BBG05] S. Baselice, P. A. Bonatti, and M. Gelfond. A preliminary report on integrating of answer set and constraint solving. In Answer Set Programming, volume 142 of CEUR Workshop Proceedings, 2005. Francesco Ricca Techniques and Systems for ASP
- 70. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [BET11] Gerhard Brewka, Thomas Eiter, and Miroslaw Truszczynski. Answer set programming at a glance. Commun. ACM, 54(12):92–103, 2011. [BKOS17] M. Banbara, B. Kaufmann, M. Ostrowski, and T. Schaub. Clingcon: The next generation. TPLP, 17(4):408–461, 2017. [BL17] M. Balduccini and Y. Lierler. Constraint answer set solver EZCSP and why integration schemas matter. TPLP, 17(4):462–515, 2017. [BMMW17] Bernhard Bliem, Marius Moldovan, Michael Morak, and Stefan Woltran. The impact of treewidth on ASP grounding and solving. In IJCAI, pages 852–858. ijcai.org, 2017. [BPEL05] Marcello Balduccini, Enrico Pontelli, Omar El-Khatib, and Hung Le. Issues in parallel execution of non-monotonic reasoning systems. Parallel Computing, 31(6):608–647, 2005. Francesco Ricca Techniques and Systems for ASP
- 71. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [CDRS17] B. Cuteri, C. Dodaro, F. Ricca, and P. Schüller. Constraints, lazy constraints, or propagators in ASP solving: An empirical analysis. TPLP, 17(5-6):780–799, 2017. [CFG+ 12] F. Calimeri, W. Faber, M. Gebser, G. Ianni, R. Kaminski, T. Krennwallner, N. Leone, F. Ricca, and T. Schaub. ASP-Core-2: Input language format. https://www.mat. unical.it/aspcomp2013/ASPStandardization/, 2012. [CFPZ17] Francesco Calimeri, Davide Fuscà, Simona Perri, and Jessica Zangari. I-DLV: the new intelligent grounder of DLV. Intelligenza Artiﬁciale, 11(1):5–20, 2017. [CGMR16] Francesco Calimeri, Martin Gebser, Marco Maratea, and Francesco Ricca. Design and results of the ﬁfth answer set programming competition. Artif. Intell., 231:151–181, 2016. Francesco Ricca Techniques and Systems for ASP
- 72. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [CHO+ 09] Ozan Caldiran, Kadir Haspalamutgil, Abdullah Ok, Can Palaz, Esra Erdem, and Volkan Patoglu. Bridging the gap between high-level reasoning and low-level control. In LPNMR, pages 342–354, 2009. [dCDBS15] Broes de Cat, Marc Denecker, Maurice Bruynooghe, and Peter J. Stuckey. Lazy model expansion: Interleaving grounding with search. J. Artif. Intell. Res., 52:235–286, 2015. [DEF+ 12] Minh Dao-Tran, Thomas Eiter, Michael Fink, Gerald Weidinger, and Antonius Weinzierl. Omiga : An open minded grounding on-the-ﬂy answer set solver. In JELIA, volume 7519 of Lecture Notes in Computer Science, pages 480–483. Springer, 2012. [DEGV01] Evgeny Dantsin, Thomas Eiter, Georg Gottlob, and Andrei Voronkov. Complexity and Expressive Power of Logic Programming. ACM Computing Surveys, 33(3):374–425, 2001. Francesco Ricca Techniques and Systems for ASP
- 73. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [DFPV16] A. Dovier, A. Formisano, E. Pontelli, and F. Vella. A GPU implementation of the ASP computation. In PADL’16, volume 9585, pages 30–47, 2016. [DGH09] James P. Delgrande, Torsten Grote, and Aaron Hunter. A general approach to the veriﬁcation of cryptographic protocols using answer set programming. In LPNMR, pages 355–367, 2009. [DGL+ 16] C. Dodaro, P. Gasteiger, N. Leone, B. Musitsch, F. Ricca, and K. Schekotihin. Combining answer set programming and domain heuristics for solving hard industrial problems (application paper). TPLP, 16(5-6):653–669, 2016. [DLL62] Martin Davis, George Logemann, and Donald W. Loveland. A machine program for theorem-proving. Commun. ACM, 5(7):394–397, 1962. Francesco Ricca Techniques and Systems for ASP
- 74. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [DW12] C. Drescher and T. Walsh. Answer set solving with lazy nogood generation. In Technical Communications of ICLP’12, pages 188–200, 2012. [EEB10] Halit Erdogan, Esra Erdem, and Olivier Bodenreider. Exploiting umls semantics for checking semantic consistency among umls concepts. In In Proc. of MedInfo, 2010. [EFI+ 16] T. Eiter, M. Fink, G. Ianni, T. Krennwallner, C. Redl, and P. Schüller. A model building framework for answer set programming with external computations. Theory and Practice of Logic Progeamming, 16(4):418–464, 2016. [EFLP99] Thomas Eiter, Wolfgang Faber, Nicola Leone, and Gerald Pfeifer. The diagnosis frontend of the dlv system. AI Commun., 12(1-2):99–111, 1999. [EGL16] Esra Erdem, Michael Gelfond, and Nicola Leone. Applications of answer set programming. AI Magazine, 37(3):53–68, 2016. Francesco Ricca Techniques and Systems for ASP
- 75. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [EGM97] Thomas Eiter, Georg Gottlob, and Heikki Mannila. Disjunctive datalog. ACM Trans. Database Syst., 22(3):364–418, 1997. [EIST06] Thomas Eiter, Giovambattista Ianni, Roman Schindlauer, and Hans Tompits. Effective integration of declarative rules with external evaluations for semantic-web reasoning. In ESWC, pages 273–287, 2006. [EL03] Esra Erdem and Vladimir Lifschitz. Tight logic programs. TPLP, 3(4-5):499–518, 2003. [FMMT01] R. Finkel, V. Marek, N. Moore, and M. Truszczy´nski. Computing stable models in parallel. In ASP’01, 2001. [For82] Charles L. Forgy. Rete: A fast algorithm for the many pattern/many object pattern match problem. Artiﬁcial Intelligence, 19(1):17 – 37, 1982. Francesco Ricca Techniques and Systems for ASP
- 76. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [GJM+ 06] J. Gressmann, T. Janhunen, R. E. Mercer, T. Schaub, S. Thiele, and R. Tichy. On probing and multi-threading in platypus. In ECAI’06, volume 141 of FAIA, pages 392–396. IOS Press, 2006. [GJR] M. Gebser, T. Janhunen, and J. Rintanen. Answer set programming as SAT modulo acyclicity. pages 351–356. [GKK+ a] M. Gebser, R. Kaminski, B. Kaufmann, M. Ostrowski, T. Schaub, and S. Thiele. Engineering an incremental ASP solver. pages 190–205. [GKK+ b] M. Gebser, R. Kaminski, B. Kaufmann, M. Ostrowski, T. Schaub, and P. Wanko. Theory solving made easy with clingo 5. pages 2:1–2:15. [GKK+ 11a] M. Gebser, R. Kaminski, B. Kaufmann, T. Schaub, M. Schneider, and S. Ziller. A portfolio solver for answer set programming: Preliminary report. In LPNMR’11, volume 6645, pages 352–357, 2011. Francesco Ricca Techniques and Systems for ASP
- 77. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [GKK+ 11b] M. Gebser, R. Kaminski, B. Kaufmann, T. Schaub, and B. Schnor. Cluster-based ASP solving with claspar. In LPNMR’11, volume 6645, pages 364–369, 2011. [GKK+ 15] M. Gebser, R. Kaminski, B. Kaufmann, J. Romero, and T. Schaub. Progress in clasp series 3. In LPNMR’15, volume 9345 of LNCS, pages 368–383. Springer, 2015. [GKK+ 16] Martin Gebser, Roland Kaminski, Benjamin Kaufmann, Max Ostrowski, Torsten Schaub, and Philipp Wanko. Theory solving made easy with clingo 5. In ICLP (Technical Communications), volume 52 of OASICS, pages 2:1–2:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. [GKKS11] Martin Gebser, Roland Kaminski, Arne König, and Torsten Schaub. Advances in gringo series 3. In LPNMR, volume 6645 of Lecture Notes in Computer Science, pages 345–351. Springer, 2011. Francesco Ricca Techniques and Systems for ASP
- 78. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [GKNS07] Martin Gebser, Benjamin Kaufmann, André Neumann, and Torsten Schaub. clasp : A conﬂict-driven answer set solver. In LPNMR, volume 4483 of Lecture Notes in Computer Science, pages 260–265. Springer, 2007. [GKS12] M. Gebser, B. Kaufmann, and T. Schaub. Multi-threaded ASP solving with clasp. TPLP, 12(4-5):525–545, 2012. [GL91] Michael Gelfond and Vladimir Lifschitz. Classical negation in logic programs and disjunctive databases. New Generation Comput., 9(3/4):365–386, 1991. [GLM06] Enrico Giunchiglia, Yuliya Lierler, and Marco Maratea. Answer set programming based on propositional satisﬁability. J. Autom. Reasoning, 36(4):345–377, 2006. [GMR17] Martin Gebser, Marco Maratea, and Francesco Ricca. The sixth answer set programming competition. J. Artif. Intell. Res., 60:41–95, 2017. Francesco Ricca Techniques and Systems for ASP
- 79. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [GNA13] Terracina Giorgio, Leone Nicola, and Martello Alessandra. Logic-based techniques for data cleaning: an application to the italian national healthcare system. LPNMR, 2013. [GST07] Martin Gebser, Torsten Schaub, and Sven Thiele. Gringo : A new grounder for answer set programming. In LPNMR, volume 4483 of Lecture Notes in Computer Science, pages 266–271. Springer, 2007. [HKLS15] Holger Hoos, Roland Kaminski, Marius Lindauer, and Torsten Schaub. aspeed: Solver scheduling via answer set programming. TPLP, 15(1):117–142, 2015. [HLS14] H. Hoos, M. Lindauer, and T. Schaub. claspfolio 2: Advances in algorithm selection for answer set programming. TPLP, 14(4-5):569–585, 2014. Francesco Ricca Techniques and Systems for ASP
- 80. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [Jan06] T. Janhunen. Some (in)translatability results for normal logic programs and propositional theories. J. of Appl. Non-Class. Log., 16(1-2):35–86, 2006. [JN11] T. Janhunen and I. Niemelä. Compact translations of non-disjunctive answer set programs to propositional clauses. In LP, KR, and NMR, volume 6565 of LNCS, pages 111–130. Springer, 2011. [JNS+ 06] Tomi Janhunen, Ilkka Niemelä, Dietmar Seipel, Patrik Simons, and Jia-Huai You. Unfolding partiality and disjunctions in stable model semantics. ACM Trans. Comput. Log., 7(1):1–37, 2006. [JNS09] T. Janhunen, I. Niemelä, and M. Sevalnev. Computing stable models via reductions to difference logic. In LPNMR’09, volume 5753, pages 142–154, 2009. Francesco Ricca Techniques and Systems for ASP
- 81. Introduction and Preliminaries Evaluation Techniques and Systems Interfaces and Systems for Extensions References References (cont.) [KLPS16] Benjamin Kaufmann, Nicola Leone, Simona Perri, and Torsten Schaub. Grounding and solving in answer set programming. AI Magazine, 37(3):25–32, 2016. [Lif02] Vladimir Lifschitz. Answer set programming and plan generation. Artif. Intell., 138(1-2):39–54, 2002. [LJN12] G. Liu, T. Janhunen, and I. Niemelä. Answer set programming via mixed integer programming. In KR’12, pages 32–42. AAAI Press, 2012. [LM04] Yuliya Lierler and Marco Maratea. Cmodels-2: Sat-based answer set solver enhanced to non-tight programs. In LPNMR, volume 2923 of Lecture Notes in Computer Science, pages 346–350. Springer, 2004. [LMR16] Yuliya Lierler, Marco Maratea, and Francesco Ricca. Systems, engineering environments, and competitions. AI Magazine, 37(3):45–52, 2016. Francesco Ricca Techniques and Systems for ASP
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