## Datalog Programs and Their Stable Models

Citations: | 2 - 0 self |

### BibTeX

@MISC{Lifschitz_datalogprograms,

author = {Vladimir Lifschitz},

title = {Datalog Programs and Their Stable Models},

year = {}

}

### OpenURL

### Abstract

Abstract. This paper is about the functionality of software systems used in answer set programming (ASP). ASP languages are viewed here, in the spirit of Datalog, as mechanisms for characterizing intensional (output) predicates in terms of extensional (input) predicates. Our approach to the semantics of ASP programs is based on the concept of a stable model defined in terms of a modification of parallel circumscription. 1

### Citations

1492 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...{q(c), q(b)}, {q(c), q(b), q(a)}. We describe here a declarative semantics for a class of ASP programs that includes many examples of this kind. Our approach is based on the concept of a stable model =-=[5]-=- generalized as proposed in [3]. We will see, for instance, that the stable models of the program from Example 1 are arbitrary interpretations (in the sense of first-order logic) of the language with ... |

847 | Classical negation in logic programs and disjunctive databases
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...s to not r(X) in logic programming notation. When we write a rule as a formula, the negation symbol ¬ corresponds to negation as failure, and not to “classical” (or “strong”) negation in the sense of =-=[6]-=-. (To represent rules containing strong negation as first-order formulas, we would have to eliminate strong negation from them in favor of additional predicate constants.) In this paper, a (Datalog) p... |

523 |
Knowledge Representation, Reasoning and Declarative Problem Solving
- Baral
(Show Context)
Citation Context ...concept of a stable model defined in terms of a modification of parallel circumscription. 1 Introduction This paper is about the functionality of software systems used in answer set programming (ASP) =-=[11, 14, 1, 7]-=-. ASP languages are viewed here, in the spirit of Datalog, as mechanisms for characterizing intensional (output) predicates in terms of extensional (input) predicates. Example 1. The ASP program q(X,Y... |

486 | Applications of circumscription to formalizing common sense knowledge
- McCarthy
(Show Context)
Citation Context ...ill call them positive. In Figure 1, the only rules that are not positive are those in lines 4 and 7. In the special case of positive programs, SMp is the well-known parallel circumscription operator =-=[12]-=-, [2, Section 6.4.2]. The definition of parallel circumscription uses the following notation. If p and q are predicate constants of the same arity then p ≤ q stands for the formula ∀x(p(x) → q(x)), wh... |

326 | Logic programming with stable model semantics as a constraint programming paradigm
- Niemelä
- 1999
(Show Context)
Citation Context ...concept of a stable model defined in terms of a modification of parallel circumscription. 1 Introduction This paper is about the functionality of software systems used in answer set programming (ASP) =-=[11, 14, 1, 7]-=-. ASP languages are viewed here, in the spirit of Datalog, as mechanisms for characterizing intensional (output) predicates in terms of extensional (input) predicates. Example 1. The ASP program q(X,Y... |

247 | Stable models and an alternative logic programming paradigm
- Marek, Truszczyński
- 1999
(Show Context)
Citation Context ...concept of a stable model defined in terms of a modification of parallel circumscription. 1 Introduction This paper is about the functionality of software systems used in answer set programming (ASP) =-=[11, 14, 1, 7]-=-. ASP languages are viewed here, in the spirit of Datalog, as mechanisms for characterizing intensional (output) predicates in terms of extensional (input) predicates. Example 1. The ASP program q(X,Y... |

194 | Strongly equivalent logic programs
- Lifschitz, Pearce, et al.
(Show Context)
Citation Context ...to two equivalent formulas, may produce non-equivalent formulas. For instance, in application to formulas (6) this transformation gives the non-equivalent formulas ⊤ → u(a), ¬p(a) → ⊥. The results of =-=[15, 9, 10, 3]-=- show, on the other hand, that replacing a group of rules within a Datalog program with another group of rules does not affectthe class of stable models whenever the two sets of rules are intuitionis... |

48 | Stable models and circumscription
- Ferraris, Lee, et al.
(Show Context)
Citation Context ...}. We describe here a declarative semantics for a class of ASP programs that includes many examples of this kind. Our approach is based on the concept of a stable model [5] generalized as proposed in =-=[3]-=-. We will see, for instance, that the stable models of the program from Example 1 are arbitrary interpretations (in the sense of first-order logic) of the language with binary predicate constants p, q... |

40 | What is answer set programming
- Lifschitz
- 2008
(Show Context)
Citation Context |

34 |
A new logical characterization of stable models and answer sets
- Pearce
- 1997
(Show Context)
Citation Context ...to two equivalent formulas, may produce non-equivalent formulas. For instance, in application to formulas (6) this transformation gives the non-equivalent formulas ⊤ → u(a), ¬p(a) → ⊥. The results of =-=[15, 9, 10, 3]-=- show, on the other hand, that replacing a group of rules within a Datalog program with another group of rules does not affectthe class of stable models whenever the two sets of rules are intuitionis... |

30 | A.: A characterization of strong equivalence for logic programs with variables
- Lifschitz, Pearce, et al.
(Show Context)
Citation Context ...to two equivalent formulas, may produce non-equivalent formulas. For instance, in application to formulas (6) this transformation gives the non-equivalent formulas ⊤ → u(a), ¬p(a) → ⊥. The results of =-=[15, 9, 10, 3]-=- show, on the other hand, that replacing a group of rules within a Datalog program with another group of rules does not affectthe class of stable models whenever the two sets of rules are intuitionis... |

11 | Knowledge representation and classical logic
- Lifschitz, Morgenstern, et al.
- 2007
(Show Context)
Citation Context ...rs of the list p. 9 Compare, for instance, the rule q(X) ; r(X) :- p(X). from Example 2 and the rule q(X) :- p(X), not r(X). The corresponding formulas ∀x(p(x) → q(x) ∨ r(x)), ∀x(p(x) ∧ ¬r(x) → q(x)) =-=(8)-=- are not intuitionistically equivalent to each other; it is not surprising then that replacing one rule by the other within a Datalog program usually changes the class of stable models. But the rules ... |

5 | On the Stable Model Semantics of First-Order Formulas with Aggregates
- Ferraris, Lifschitz
- 2010
(Show Context)
Citation Context ...than #count, such as #sum (the sum of a set of integers). It appears that such “difficult” aggregates can be handled by extending the operator SM to expressions more general than first-order formulas =-=[4]-=-. Acknowledgements I am grateful to Paolo Ferraris, Joohyung Lee, Yuliya Lierler, Fangkai Yang, and the anonymous referee for useful comments. This work was partially supported by the National Science... |

4 |
Ilkka Niemelä, and Miroslaw Truszczynski. Answer set programming at a glance
- Brewka
(Show Context)
Citation Context ...ets is proper. In second-order logic, we apply the same notation to tuples of predicate variables. For any positive Datalog program (F, p), we define SMp[F ] as the sentence F ∧ ¬∃u((u < p) ∧ F (u)), =-=(2)-=- where u is a list of distinct predicate variables of the same length as p, and F (u) is the formula obtained from F by substituting the variables u for the constants p. The second conjunctive term of... |

2 | Intuitionistic logic
- Moschovakis
- 2008
(Show Context)
Citation Context ...erraris, Joohyung Lee, Yuliya Lierler, Fangkai Yang, and the anonymous referee for useful comments. This work was partially supported by the National Science Foundation under grant IIS-0712113. 8 See =-=[13]-=- for an introduction to intuitionistic logic. 9 This assertion will remain true if we allow F in (7) to have occurrences of intensional predicates as long as each of them is in the scope of a negation... |

1 | Stable models and circumscription 12 - Ferraris, Lee, et al. |