## Constraint Answer Set Solving

Citations: | 34 - 5 self |

### BibTeX

@MISC{Gebser_constraintanswer,

author = {Martin Gebser and Max Ostrowski and Torsten Schaub},

title = {Constraint Answer Set Solving},

year = {}

}

### OpenURL

### Abstract

Abstract. We present a new approach to integrating Constraint Processing (CP) techniques into Answer Set Programming (ASP). Based on an alternative semantic approach, we develop an algorithmic framework for conflict-driven ASP solving that exploits CP solving capacities. A significant technical issue concerns the combination of conflict information from different solver types. We have implemented our approach, combining ASP solver clingo with the generic CP solver gecode, and we empirically investigate its computational impact. 1

### Citations

599 |
Constraint Processing
- Dechter
- 2003
(Show Context)
Citation Context ...t a non-trivial reason (one that does not include all previously assigned literals over C) from structural properties of CSP[P ]. Our approach for this is inspired by graph-based backjumping/learning =-=[10]-=- where, for a variable in question, other variables it shares constraints with are con-sidered as potential reasons. In fact, we identify a sufficient reason by considering all literals over atom(P )... |

546 |
Knowledge Representation, Reasoning and Declarative Problem Solving
- Baral
(Show Context)
Citation Context ...s. We have implemented our approach, combining ASP solver clingo with the generic CP solver gecode, and we empirically investigate its computational impact. 1 Introduction Answer Set Programming (ASP;=-=[1]-=-) is a declarative problem solving approach, combining a rich yet simple modeling language with high-performance solving capacities. This has already resulted in various applications, among them decis... |

399 | GRASP: A Search Algorithm for Propositional Satisfiability
- Marques-Silva, Sakallah
- 1999
(Show Context)
Citation Context ... “oracle.” The basic algorithm for finding standard answer sets is called Conflict-Driven Nogood Learning (CDNL); it includes conflict-driven learning and backjumping according to the FirstUIP scheme =-=[21, 22, 7]-=-. That is, whenever a conflict happens, a conflict nogood containing a Unique Implication Point (UIP) is identified by iteratively resolving a violated nogood against a second nogood that is a reason ... |

320 | Extending and implementing the stable model semantics
- Simons, Niemelä, et al.
(Show Context)
Citation Context ...high-level algorithm viewing both ASP and CP solvers as black boxes, [14] embeds a CP solver into a traditional DPLL-style backtracking algorithm, similar to the one underlying the ASP solver smodels =-=[15]-=-. Although [12– 14] resulted in two consecutive extensions of smodels with CP capacities, they do not match the performance of state-of-the-art SMT solvers, simply because they do not support advanced... |

306 | Efficient conflict driven learning in a boolean satisfiability solver
- Zhang, Madigan, et al.
- 2001
(Show Context)
Citation Context ... “oracle.” The basic algorithm for finding standard answer sets is called Conflict-Driven Nogood Learning (CDNL); it includes conflict-driven learning and backjumping according to the FirstUIP scheme =-=[21, 22, 7]-=-. That is, whenever a conflict happens, a conflict nogood containing a Unique Implication Point (UIP) is identified by iteratively resolving a violated nogood against a second nogood that is a reason ... |

156 | Solving SAT and SAT Modulo Theories: from an Abstract Davis-Putnam-Logemann-Loveland Procedure to DPLL(T
- Nieuwenhuis, Oliveras, et al.
(Show Context)
Citation Context ...large domains avoids the grounding bottleneck inherent to all propositional solving approaches. In Satisfiability checking (SAT;[7, 8]), this led to the subarea of Satisfiability Modulo Theories (SMT;=-=[9]-=-), extending SAT solvers by theory-specific solvers. This allows SMT problems to incorporate predicates from specialized theories into propositional formulas. Solving an SMT problem then consists of f... |

147 | Consistency of Clark’s completion and existence of stable models
- Fages
- 1993
(Show Context)
Citation Context ...ine 12). Finally, flag cp is set in Line 13 if σ is over an atom of C. After reaching a fixpoint of unit propagation without any conflict, unfounded set handling (cf. [19]) is performed for non-tight =-=[23]-=- programs in Line 17–19. Note that an already identified nonempty unfounded set needs first to be falsified completely before a new (nonempty) unfounded set U ⊆ atom(P )|A \ A F is determined in Line ... |

126 | Conflict-driven answer set solving
- Gebser, Kaufmann, et al.
- 2007
(Show Context)
Citation Context ...s the ⊆-smallest model of the reduct P X = {head(r) ← body(r) + | r ∈ P, body(r) − ∩ X = ∅}. An answer set can also be seen as a Boolean assignment satisfying all conditions induced by program P (cf. =-=[19]-=-). A constraint satisfaction problem (CSP) is a triple (V, D, C), where V is a set of variables with respective domains D, and C is a set of constraints. Each variable v ∈ V has an associated domain d... |

72 | An A-Prolog decision support system for the space shuttle
- Balduccini, Gelfond, et al.
- 2001
(Show Context)
Citation Context ...ining a rich yet simple modeling language with high-performance solving capacities. This has already resulted in various applications, among them decision support systems for NASA shuttle controllers =-=[2, 3]-=- and various reasoning tools in systems biology [4– 6]. However, certain aspects of such applications are more naturally modeled by additionally using non-Boolean constructs, accounting for resources,... |

44 |
A knowledge based approach for representing and reasoning about signaling networks
- Baral, Chancellor, et al.
- 2004
(Show Context)
Citation Context ...–(12). This is an authentic program, processable by our solver; its syntax extends the input language of gringo [20] and thus allows for using integral ranges, asin (2), and cardinality rules, as in =-=(4)-=-. For simplicity, we omit domain atoms bucket(B), bucket(C), and time(T ), respectively, in rules (5)–(10): time(0..tmax ) (2) bucket(a) bucket(b) (3) 1 {pour(B, T ) : bucket(B)} 1 ← time(T ), T < tma... |

35 | Towards an integration of answer set and constraint solving
- Bonatti, Gelfond
- 2005
(Show Context)
Citation Context ...cessing (CP;[10, 11]) techniques was conducted in [12–14]. Based on firm semantic underpinnings, these approaches provide a family of ASP languages parametrized by different constraint classes. While =-=[12]-=- develops a high-level algorithm viewing both ASP and CP solvers as black boxes, [14] embeds a CP solver into a traditional DPLL-style backtracking algorithm, similar to the one underlying the ASP sol... |

30 | A user’s guide to gringo, clasp, clingo, and iclingo. Unpublished draft, 2008. Available at http://downloads.sourceforge.net/potassco/guide.pdf?use_mirror - Gebser, Kaminski, et al. |

29 | Integrating answer set programming and constraint logic programming
- Mellarkod, Gelfond, et al.
(Show Context)
Citation Context ...erpinnings, these approaches provide a family of ASP languages parametrized by different constraint classes. While [12] develops a high-level algorithm viewing both ASP and CP solvers as black boxes, =-=[14]-=- embeds a CP solver into a traditional DPLL-style backtracking algorithm, similar to the one underlying the ASP solver smodels [15]. Although [12– 14] resulted in two consecutive extensions of smodels... |

23 | Answer set based design of knowledge systems
- Balduccini, Gelfond, et al.
- 2006
(Show Context)
Citation Context ...ining a rich yet simple modeling language with high-performance solving capacities. This has already resulted in various applications, among them decision support systems for NASA shuttle controllers =-=[2, 3]-=- and various reasoning tools in systems biology [4– 6]. However, certain aspects of such applications are more naturally modeled by additionally using non-Boolean constructs, accounting for resources,... |

16 | P.: Detecting inconsistencies in large biological networks with answer set programming. TPLP
- Gebser, Schaub, et al.
- 2011
(Show Context)
Citation Context ...rules (5)–(10): time(0..tmax ) (2) bucket(a) bucket(b) (3) 1 {pour(B, T ) : bucket(B)} 1 ← time(T ), T < tmax (4) 1 ≤ $ amt(B, T ) ← pour(B, T ), T < tmax (5) amt(B, T ) ≤ $ 3 ← pour(B, T ), T < tmax =-=(6)-=- amt(B, T ) = $ 0 ← not pour(B, T ), T < tmax (7) vol(B, T +1) = $ vol(B, T ) + amt(B, T ) ← T < tmax (8) down(B, T ) ← vol(C, T ) < $ vol(B, T ) (9) up(B, T ) ← not down(B, T ) (10) vol(a, 0) = $ 0 v... |

14 |
A SAT solver primer. Bulletin of the European Association for Theoretical Computer
- Mitchell
(Show Context)
Citation Context ...s, or functions over finite domains. Moreover, a dedicated treatment of large domains avoids the grounding bottleneck inherent to all propositional solving approaches. In Satisfiability checking (SAT;=-=[7, 8]-=-), this led to the subarea of Satisfiability Modulo Theories (SMT;[9]), extending SAT solvers by theory-specific solvers. This allows SMT problems to incorporate predicates from specialized theories i... |

12 |
G.: External sources of knowledge and value invention in logic programming
- Calimeri, Cozza, et al.
- 2007
(Show Context)
Citation Context ...orts incremental solving and backtracking. Unlike this, we use with gecode an off-the-shelf CP system. Although it is incremental, backtracking and reason generation must be dealt with externally. In =-=[24]-=-, “functional oracles” allow for computing instantiations of so-called external predicates during grounding. Constraint atoms in our sense can also be viewed as being external to some extent, given th... |

11 |
Integrating answer set reasoning with constraint solving techniques
- Mellarkod, Gelfond
- 2008
(Show Context)
Citation Context ...nt variables. Also, [12– 14] use traditional ASP solving algorithms, based on DPLL-style backtracking. In fact, adsolver’s implementation relies on lparse and smodels. The implementation described in =-=[13]-=- allows the usage of difference constraints of the form X −Y > k for variables X, Y and constant k; at most one such constraint is allowed within an integrity constraint. The underlying CP solver is h... |