## Discovering Classes of Strongly Equivalent Logic Programs (2005)

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Venue: | In: Proc. of the Intl. Joint Conf. on Artificial Intelligence (IJCAI’05 |

Citations: | 20 - 5 self |

### BibTeX

@INPROCEEDINGS{Lin05discoveringclasses,

author = {Fangzhen Lin and Yin Chen},

title = {Discovering Classes of Strongly Equivalent Logic Programs},

booktitle = {In: Proc. of the Intl. Joint Conf. on Artificial Intelligence (IJCAI’05},

year = {2005},

pages = {516--521}

}

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### Abstract

In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules. 1.

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Citation Context ...e the set {h1, ..., hk}, Psr the set {p1, ..., pm}, and Ngr the set {pm+1, ..., pn}. Thus a rule r can also be written as Hdr ← Psr, not Ngr. The semantics of these programs are given by answer sets (=-=Gelfond & Lifschitz, 1991-=-), which 432 (1)sDiscovering Classes of Strongly Equivalent Logic Programs are defined by a fixed-point operator through what has been known as Gelfond-Lifschitz transformation. Let X be a subset of L... |

345 | The DLV system for knowledge representation and reasoning
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Citation Context ...gramming paradigms, ASP allows natural encodings of recursive relations, and has built-in facilities for default reasoning. Several ASP solvers have been developed (Niemelä, Simons, & Syrjänen, 2000; =-=Leone, Pfeifer, Faber, Eiter, Gottlob, Perri, & Scarcello, 2006-=-; Lin & Zhao, 2004; Lierler & Maratea, 2004). To date, ASP has been used in space shuttle planning (Nogueira, Balduccini, Gelfond, Watson, & Barry, 2001), evolutional linguistics (Erdem, Lifschitz, Na... |

334 | Logic programs with stable model semantics as a constraint programming paradigm
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Citation Context ...solve problems by query answering. The user encodes knowledge about a domain by a set of rules, and solves a problem by issuing queries to the set of rules. In contrast, Answer Set Programming (ASP) (=-=Niemelä, 1999-=-; Lifschitz, 1999; Marek & Truszczynski, 1999) is a constraint-based programming paradigm. It is based on logic programming with answer set semantics (Gelfond & Lifschitz, 1988, 1991). To solve a prob... |

213 | ASSAT: Computing answer sets of a logic program by SAT solvers
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(Show Context)
Citation Context ...ations, and has built-in facilities for default reasoning. Several ASP solvers have been developed (Niemelä, Simons, & Syrjänen, 2000; Leone, Pfeifer, Faber, Eiter, Gottlob, Perri, & Scarcello, 2006; =-=Lin & Zhao, 2004-=-; Lierler & Maratea, 2004). To date, ASP has been used in space shuttle planning (Nogueira, Balduccini, Gelfond, Watson, & Barry, 2001), evolutional linguistics (Erdem, Lifschitz, Nakhleh, & Ringe, 20... |

205 | Strongly equivalent logic programs
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Citation Context ...th {a} and {b, c} are answer sets, and they are the only answer sets of the program. Two logic programs P1 and P2 are said to be equivalent if they have the same answer sets, and strongly equivalent (=-=Lifschitz et al., 2001-=-) (under the language L), written P1 �se P2, if for any logic program P in L, P ∪ P1 and P ∪ P2 are equivalent (thus we write P1 ��se P2 when P1 and P2 are not strongly equivalent). For example, {a ← ... |

79 | Cmodels-2: SAT-based answer set solver enhanced to non-tight programs
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Citation Context ...ilt-in facilities for default reasoning. Several ASP solvers have been developed (Niemelä, Simons, & Syrjänen, 2000; Leone, Pfeifer, Faber, Eiter, Gottlob, Perri, & Scarcello, 2006; Lin & Zhao, 2004; =-=Lierler & Maratea, 2004-=-). To date, ASP has been used in space shuttle planning (Nogueira, Balduccini, Gelfond, Watson, & Barry, 2001), evolutional linguistics (Erdem, Lifschitz, Nakhleh, & Ringe, 2003), and others. In the f... |

62 | Strong equivalence made easy: Nested expressions and weight constraints. Theory and Practice of Logic Programming - Turner |

58 |
Reducing strong equivalence of logic programs to entailment in classical propositional logic
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Citation Context ...nerating example pairs of strongly equivalent logic programs, and for verifying a conjecture. We repeat it here. Let P1 and P2 be two finite logic programs, and L the set of atoms in them. Theorem 1 (=-=Lin, 2002-=-) P1 �se P2 iff in propositional logic, the following sentence is valid: ( � p ⊃ p ′ ) ⊃ [ � δ(r) ≡ � δ(r)], (2) p∈L r∈P1 where for each p ∈ L, p ′ is a new atom, and for each rule r of the form (1), ... |

57 | Semantics of (disjunctive) logic programs based on partial evaluation
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Citation Context ...using the results that we have here for program simplification. Indeed, transformation rules such as deleting those that contain common elements in their heads and positive bodies have been proposed (=-=Brass & Dix, 1999-=-), and studied from the perspective of strong equivalence (Osorio et al., 2001; Eiter et al., 2004). Our results add new such transformation rules. For instance, by Theorem 7, we can delete those elem... |

48 |
Encodings for equilibrium logic and logic programs with nested expressions
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Citation Context ...and if k = 0, then the right sides of the implications in (3) and (4) are considered to be false. In general checking if two sets of rules are strongly equivalent is coNP-complete (c.f. Turner, 2001; =-=Pearce, Tompits, & Woltran, 2001-=-; Lin, 2002). 3. The Problem As we mentioned above, one possible use of the notion of strongly equivalent logic programs is in program simplification. For instance, given a logic program, for each rul... |

44 | Smodels: A system for answer set programming
- Niemelä, Simons, et al.
- 2000
(Show Context)
Citation Context ...pared to other constraint-based programming paradigms, ASP allows natural encodings of recursive relations, and has built-in facilities for default reasoning. Several ASP solvers have been developed (=-=Niemelä, Simons, & Syrjänen, 2000-=-; Leone, Pfeifer, Faber, Eiter, Gottlob, Perri, & Scarcello, 2006; Lin & Zhao, 2004; Lierler & Maratea, 2004). To date, ASP has been used in space shuttle planning (Nogueira, Balduccini, Gelfond, Wats... |

37 | Simplifying logic programs under uniform and strong equivalence
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- 2004
(Show Context)
Citation Context ... as deleting those that contain common elements in their heads and positive bodies have been proposed (Brass & Dix, 1999), and studied from the perspective of strong equivalence (Osorio et al., 2001; =-=Eiter et al., 2004-=-). Our results add new such transformation rules. For instance, by Theorem 7, we can delete those elements in the head of a rule that also appear in the negation-as-failure part of the rule. Theorems ... |

33 |
Action languages, Answer Sets, and Planning. In The Logic Programming Paradigm: a 25-Year Perspective
- Lifschitz
- 1999
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Citation Context ...by query answering. The user encodes knowledge about a domain by a set of rules, and solves a problem by issuing queries to the set of rules. In contrast, Answer Set Programming (ASP) (Niemelä, 1999; =-=Lifschitz, 1999-=-; Marek & Truszczynski, 1999) is a constraint-based programming paradigm. It is based on logic programming with answer set semantics (Gelfond & Lifschitz, 1988, 1991). To solve a problem, the user enc... |

31 |
On Automated Scientific Theory Formation: A Case Study Using the AM Program
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- 1979
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Citation Context ...es, and aims at finding a theory that would explain the given examples/consequences. Using computers to discover theorems is an old aspiration. There have been some success stories. For instance, AM (=-=Lenat, 1979-=-) was reported to be able to come up with some interesting concepts and theorems in number theory, and the remarkable systems described by Petkovsek, Wilf, and Zeilberger (1996) can discover many iden... |

27 | Strong equivalence for logic programs and default theories (made easy
- Turner
(Show Context)
Citation Context ...d to be true, and if k = 0, then the right sides of the implications in (3) and (4) are considered to be false. In general checking if two sets of rules are strongly equivalent is coNP-complete (c.f. =-=Turner, 2001-=-; Pearce, Tompits, & Woltran, 2001; Lin, 2002). 3. The Problem As we mentioned above, one possible use of the notion of strongly equivalent logic programs is in program simplification. For instance, g... |

22 | Equivalence in Answer Set Programming
- Osorio, Navarro, et al.
- 2001
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Citation Context ...sformation rules such as deleting those that contain common elements in their heads and positive bodies have been proposed (Brass & Dix, 1999), and studied from the perspective of strong equivalence (=-=Osorio et al., 2001-=-; Eiter et al., 2004). Our results add new such transformation rules. For instance, by Theorem 7, we can delete those elements in the head of a rule that also appear in the negation-as-failure part of... |

20 | Equivalence of logic programs under updates - Inoue, Sakama - 2004 |

19 | Reconstructing the evolutionary history of indo-european languages using answer set programming
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Citation Context ...i, & Scarcello, 2006; Lin & Zhao, 2004; Lierler & Maratea, 2004). To date, ASP has been used in space shuttle planning (Nogueira, Balduccini, Gelfond, Watson, & Barry, 2001), evolutional linguistics (=-=Erdem, Lifschitz, Nakhleh, & Ringe, 2003-=-), and others. In the following, we briefly review some basic notions in ASP. Let L be a propositional language, i.e. a set of atoms. In this paper we shall consider logic programs with rules of the f... |

18 |
Stable logic programming - an alternative logic programming paradigm
- Marek, Truszczynski
- 1999
(Show Context)
Citation Context ...g. The user encodes knowledge about a domain by a set of rules, and solves a problem by issuing queries to the set of rules. In contrast, Answer Set Programming (ASP) (Niemelä, 1999; Lifschitz, 1999; =-=Marek & Truszczynski, 1999-=-) is a constraint-based programming paradigm. It is based on logic programming with answer set semantics (Gelfond & Lifschitz, 1988, 1991). To solve a problem, the user encodes the domain knowledge as... |

14 | Comparisons and computation of well-founded semantics for disjunctive logic programs - Wang, Zhou - 2005 |

12 | SELP - a system for studying strong equivalence between logic programs
- Chen, Lin, et al.
- 2005
(Show Context)
Citation Context ...the following result, which took about 10 hours on a Solaris server consisting of 8 Sun Ultra-SPARC III 900Mhz CPUs with 8GB RAM. For more details on the experiment on 2-1-0 problem, please refer to (=-=Chen, Lin, & Li, 2005-=-). 442sDiscovering Classes of Strongly Equivalent Logic Programs Lemma 6 For any three canonical rules r1, r2 and r3 that mention at most six atoms, {r1, r2, r3} �se {r1, r2} iff one of the following ... |

9 |
Discovering state invariants
- Lin
- 2004
(Show Context)
Citation Context ... with this work, we are one step closer to making discovering classes of strongly equivalent logic programs a Science. We have mentioned that the methodology used in this paper is similar to that in (=-=Lin, 2004-=-). In both cases, plausible conjectures are generated by testing them in domains of small sizes, and general theorems are proved to aid the verification of these conjectures in the general case. Howev... |

1 |
Discovering Classes of Strongly Equivalent Logic Programs
- Nogueira, Balduccini, et al.
- 2001
(Show Context)
Citation Context ... (Niemelä, Simons, & Syrjänen, 2000; Leone, Pfeifer, Faber, Eiter, Gottlob, Perri, & Scarcello, 2006; Lin & Zhao, 2004; Lierler & Maratea, 2004). To date, ASP has been used in space shuttle planning (=-=Nogueira, Balduccini, Gelfond, Watson, & Barry, 2001-=-), evolutional linguistics (Erdem, Lifschitz, Nakhleh, & Ringe, 2003), and others. In the following, we briefly review some basic notions in ASP. Let L be a propositional language, i.e. a set of atoms... |