## The nomore++ approach to answer set solving (2005)

Venue: | PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON LOGIC FOR PROGRAMMING, ARTIFICIAL INTELLIGENCE, AND REASONING |

Citations: | 22 - 11 self |

### BibTeX

@INPROCEEDINGS{Anger05thenomore++,

author = {Christian Anger and Martin Gebser and Thomas Linke and André Neumann and Torsten Schaub},

title = {The nomore++ approach to answer set solving},

booktitle = {PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON LOGIC FOR PROGRAMMING, ARTIFICIAL INTELLIGENCE, AND REASONING},

year = {2005},

pages = {95--109},

publisher = {Springer}

}

### OpenURL

### Abstract

We present a new answer set solver, called nomore++, along with its underlying theoretical foundations. A distinguishing feature is that it treats heads and bodies equitably as computational objects. Apart from its operational foundations, we show how it improves on previous work through its new lookahead and its computational strategy of maintaining unfounded-freeness. We underpin our claims by selected experimental results.

### Citations

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Citation Context ...der to be comparable to smodels’ assignment X. Concluding with basic propagation, we mention that P corresponds to Fitting’s operator [7], (PB) coincides to unit propagation on a program’s completion =-=[8]-=-, (PU) amounts to propagation via well-founded semantics [6], and (PBU) matches smodels’ propagation, that is, well-founded semantics enhanced by backward propagation. 5 The situation that a body is i... |

857 | The well-founded semantics for general logic programs
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Citation Context ... T ♭ (A5) B(A6) = A7 = A3 ⊔ ({d}, {{c}, c, body(r3)}) by B ♭ (A6) B(A7) = B ∗ (A3) = A3 ⊔ ({d, body(r4)}, {{c}, c, body(r3)}) by T ♭ (A7) The next definition elucidates the notion of an unfounded set =-=[6]-=- in our context. Given an assignment A, the greatest unfounded set of heads and bodies, UΠ(A), is defined in terms of the still potentially derivable atoms in U Π(A). Definition 5. Let Π be a logic pr... |

338 | The relative efficiency of propositional proof systems
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Citation Context .... Although we cannot provide the details here, it is noteworthy to mention that allowing X = head(Π) ∪ body(Π) as choices leads to an exponentially stronger proofssystem (in terms of proof complexity =-=[10]-=-, i.e. minimal proofs for unsatisfiability) in comparison to either X = head(Π) or X = body(Π). The comparison between different proof systems and proof complexity results will be key issues in the fu... |

337 | F.: The dlv system for knowledge representation and reasoning
- Leone, Pfeifer, et al.
- 2006
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Citation Context ...ur claims by selected experimental results. 1 Introduction A large part of the success of Answer Set Programming (ASP) is owed to the early availability of efficient solvers, like smodels [1] and dlv =-=[2]-=-. Since then, many other systems, sometimes following different approaches, have emerged, among them assat [3], cmodels [4], and noMoRe [5]. We present a new ASP solver, called nomore++, along with it... |

315 | Extending and implementing the stable model semantics
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Citation Context ...e underpin our claims by selected experimental results. 1 Introduction A large part of the success of Answer Set Programming (ASP) is owed to the early availability of efficient solvers, like smodels =-=[1]-=- and dlv [2]. Since then, many other systems, sometimes following different approaches, have emerged, among them assat [3], cmodels [4], and noMoRe [5]. We present a new ASP solver, called nomore++, a... |

202 | ASSAT: Computing answer sets of a logic program by SAT solvers
- Lin, Zhao
- 2004
(Show Context)
Citation Context ...ng (ASP) is owed to the early availability of efficient solvers, like smodels [1] and dlv [2]. Since then, many other systems, sometimes following different approaches, have emerged, among them assat =-=[3]-=-, cmodels [4], and noMoRe [5]. We present a new ASP solver, called nomore++, along with its underlying theoretical foundations. nomore++ pursues a hybrid approach in combining features from literal-ba... |

146 | Consistency of Clark’s completion and existence of stable models
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- 1994
(Show Context)
Citation Context ...ve reasoning, e.g. Hamiltonian cycles, this allows for more elegant and compact encodings in logic programming than in propositional logic. Such logic programming encodings produce non-tight programs =-=[11, 12]-=-, for which there is a mismatch between answer sets and the models of programs’ completions [8]. The mismatch is due to the potential of circular support among atoms. Such circularity is prohibited by... |

108 | Fixpoint semantics for logic programming — A survey
- Fitting
(Show Context)
Citation Context ...d once in 2. is that initially A assigns no values to bodies in order to be comparable to smodels’ assignment X. Concluding with basic propagation, we mention that P corresponds to Fitting’s operator =-=[7]-=-, (PB) coincides to unit propagation on a program’s completion [8], (PU) amounts to propagation via well-founded semantics [6], and (PBU) matches smodels’ propagation, that is, well-founded semantics ... |

76 | F.: Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics and Computation
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Citation Context ...y than using bodies. 15 nomore++’s strategy of maintaining unfounded-freeness is closely related to some concepts used in dlv, but still different. In fact, the term “unfounded-free” is borrowed from =-=[20]-=-, where it is used for assessing the complexity of unfounded set checks and characterising answer sets in the context of disjunctive logic programs. We, however, address assignments in which the non-c... |

75 | Cmodels-2: SAT-based Answer Set Solver Enhanced to Non-tight Programs
- LIERLER, MARATEA
(Show Context)
Citation Context ...wed to the early availability of efficient solvers, like smodels [1] and dlv [2]. Since then, many other systems, sometimes following different approaches, have emerged, among them assat [3], cmodels =-=[4]-=-, and noMoRe [5]. We present a new ASP solver, called nomore++, along with its underlying theoretical foundations. nomore++ pursues a hybrid approach in combining features from literal-based approache... |

35 |
V.: Tight logic programs. Theory and Practice of Logic Programming 3
- Erdem, Lifschitz
- 2003
(Show Context)
Citation Context ...ve reasoning, e.g. Hamiltonian cycles, this allows for more elegant and compact encodings in logic programming than in propositional logic. Such logic programming encodings produce non-tight programs =-=[11, 12]-=-, for which there is a mismatch between answer sets and the models of programs’ completions [8]. The mismatch is due to the potential of circular support among atoms. Such circularity is prohibited by... |

30 | Pushing goal derivation in DLP computations
- Faber, Leone, et al.
- 1999
(Show Context)
Citation Context ...n A ⊕ due to P. All other bodies either contain a false literal and are in A ⊖ due to P, or they positively depend on unfounded atoms in U(A) and are in A ⊖ due to U. 11 Similar to dlv’s must-be-true =-=[13]-=-; see Section 7.s⊕, while operators B, C, and L can only assign ⊗ (or ⊖). 12 Any head or body in A ⊗ can be turned into ⊕ by P without causing a conflict. So, by distinguishing two types of “true”, we... |

20 |
Pruning operators for answer set programming systems
- Calimeri, Faber, et al.
- 2002
(Show Context)
Citation Context ...between techniques used by different ASP solvers. Operators capturing propagation in dlv are given in [18]. Pruning operators based on Fitting’s [7] and well-founded semantics [6] are investigated in =-=[19]-=-. The full paper contains a detailed comparison of these operators. smodels [1] and dlv [2] pursue a literal-based approach, which boils down to restricting the domain of assignments to head(Π). Howev... |

15 |
Enhancing Efficiency and Expressiveness in Answer Set Programming Systems
- Faber
- 2002
(Show Context)
Citation Context ...re for the first time. 14 In general, operator-based specifications facilitate formal comparisons between techniques used by different ASP solvers. Operators capturing propagation in dlv are given in =-=[18]-=-. Pruning operators based on Fitting’s [7] and well-founded semantics [6] are investigated in [19]. The full paper contains a detailed comparison of these operators. smodels [1] and dlv [2] pursue a l... |

8 | Graphs and colorings for answer set programming: Abridged report
- KONCZAK, SCHAUB, et al.
- 2003
(Show Context)
Citation Context ...igned ⊕, too. The observation that assigning ⊖ to heads and ⊕ to bodies, respectively, subsumes the opposite assignments also fortifies nomore++’s lookahead strategy, detailed in Section 4. Following =-=[9]-=-, we characterise the process of answer set formation by a sequence of assignments. Theorem 2. Let Π be a logic program, let A be a total assignment of head(Π) ∪ body(Π), and let X = head(Π) ∪ body(Π)... |

5 |
NoMoRe: A System for Non-Monotonic Reasoning under Answer Set Semantics
- Anger, Konczak, et al.
(Show Context)
Citation Context ... availability of efficient solvers, like smodels [1] and dlv [2]. Since then, many other systems, sometimes following different approaches, have emerged, among them assat [3], cmodels [4], and noMoRe =-=[5]-=-. We present a new ASP solver, called nomore++, along with its underlying theoretical foundations. nomore++ pursues a hybrid approach in combining features from literal-based approaches, like smodels ... |

3 | The Nomore++ system
- Anger, Gebser, et al.
(Show Context)
Citation Context ...lpful comments. This work was supported by DFG under grant SCHA 550/6-4 as well as the EC through IST-2001-37004 WASP project. 14 Short or preliminary, respectively, notes on nomore++ can be found in =-=[16, 17]-=-. 15 The number of unique bodies in a program is always less than or equal to the number of rules. 16 Note that literal-based solvers, such as smodels and dlv, suffer from exponential worst-case compl... |