## Classical Negation in Logic Programs and Disjunctive Databases (1991)

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Venue: | New Generation Computing |

Citations: | 868 - 73 self |

### BibTeX

@ARTICLE{Gelfond91classicalnegation,

author = {Michael Gelfond and Vladimir Lifschitz},

title = {Classical Negation in Logic Programs and Disjunctive Databases},

journal = {New Generation Computing},

year = {1991},

volume = {9},

pages = {365--385}

}

### Years of Citing Articles

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### Abstract

An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter. 1 Introduction An important limitation of traditional logic programming as a knowledge representation tool, in comp...

### Citations

1876 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...nded programs, we can distinguish between a query which fails in the sense that it does not succeed and a query which fails in the stronger sense that its negation succeeds. 1 A general logic program =-=[Lloyd1984] can be de-=-fined as a set of rules of the form A 0 / A 1 ; : : : ; Am ; not Am+1 ; : : : ; not A n ; where nsms0, and each A i is an atom. The word "general" stresses the fact that such rules may conta... |

1519 | The stable model semantics for logic programming - Gelfond, Lifschitz - 1988 |

1452 |
A logic for default reasoning
- Reiter
- 1980
(Show Context)
Citation Context ...ch of two opposite predicates will be represented by a predicate constant, and which one will be considered negative. In this sense, the language of extended programs is symmetric, like default logic =-=[Reiter1980]-=-, autoepistemic logic [Moore1985] and formula circumscription [McCarthy1986]. On the contrary, the modification of our approach proposed in [Kowalski and Sadri1990] is not symmetric. In Section 6 we s... |

857 | The well-founded semantics for general logic programs - Gelder, Ross, et al. - 1991 |

491 | Applications of circumscription to formalizing common sense knowledge
- McCarthy
- 1986
(Show Context)
Citation Context ... and which one will be considered negative. In this sense, the language of extended programs is symmetric, like default logic [Reiter1980], autoepistemic logic [Moore1985] and formula circumscription =-=[McCarthy1986]-=-. On the contrary, the modification of our approach proposed in [Kowalski and Sadri1990] is not symmetric. In Section 6 we say more on the use of the closed world assumption in extended programs. Here... |

447 |
Semantical considerations on nonmonotonic logic
- Moore
- 1985
(Show Context)
Citation Context ... be represented by a predicate constant, and which one will be considered negative. In this sense, the language of extended programs is symmetric, like default logic [Reiter1980], autoepistemic logic =-=[Moore1985]-=- and formula circumscription [McCarthy1986]. On the contrary, the modification of our approach proposed in [Kowalski and Sadri1990] is not symmetric. In Section 6 we say more on the use of the closed ... |

383 | Bilattices and the semantics of logic programming
- Fitting
- 1991
(Show Context)
Citation Context ... known about A. We will return to this point in the next section, and then again in Section 6. We think of answer sets as incomplete theories (rather than "threevalued models," used, for ins=-=tance, in [Fitting1985]-=-, [Przymusinski1989] and [Van Gelder et al.1990]). When a program has several answer sets, it is incomplete also in another sense---it has several different interpretations, and the answer to a query ... |

340 | Logic programs with classical negation - Gelfond, Lifschitz - 1990 |

275 |
On closed world data bases
- Reiter
- 1987
(Show Context)
Citation Context .... 3 The difference between not P and :P in a logic program is essential whenever we cannot assume that the available positive information about P is complete, i.e., when the "closed world assumpt=-=ion" [Reiter1978]-=- is not applicable to P . The closed world assumption for a predicate P can be expressed in the language of extended programs by the rule :P (x) / not P (x): (3) When this rule is included in the prog... |

110 |
On strati autoepistemic theories
- Gelfond
- 1987
(Show Context)
Citation Context ...n instance of the general transformation 5 7! 5 + . 5. Historically, two of these reductions were proposed earlier than the definition of stable models. A reduction to autoepistemic logic is given in =-=[Gelfond1987]-=-, and the equivalence of the stable model approach to this semantics is established in [Gelfond and Lifschitz1988] (Theorem 3). A reduction to default logic is described in [Bidoit and Froidevaux1987]... |

96 |
Extended stable semantics for normal and disjunctive programs
- Przymusinski
- 1990
(Show Context)
Citation Context ...ds has received much attention in recent years. Many attempts have been made to define a declarative semantics for "disjunctive logic programs," or "disjunctive databases"; referen=-=ces can be found in [Przymusinski1990]-=-. Consider a simple example. Jack is employed by Stanford University or by SRI International; any employed individual has an adequate income. It follows that Jack has an adequate income. It would be e... |

81 | Logic programs with exceptions - Kowalski, Sadri - 1990 |

72 |
On inde data bases and the closed world assumption
- Minker
- 1982
(Show Context)
Citation Context ...onal generality, because an axiom F can be identified with the default true : =F . 9. For databases without classical negation, this definition is equivalent to the definition of a minimal model from =-=[Minker1982]-=-. 10. This definition is roughly equivalent to the construction described in Section 6 of [Przymusinski1990], applied to the stable model semantics. (Contradictory programs are treated by Przymusinski... |

66 | Paraconsistent logic programming - Blair, Subrahmanian - 1989 |

56 | Formalizing Common Sense: Papers by - McCarthy - 1990 |

42 | Minimalism subsumes default logic and circumscription - Bidoit, Froidevaux - 1987 |

35 | Compiling circumscriptive theories into logic programs - Gelfond, Lifschitz - 1989 |

35 | Argument systems: a uniform basis for nonmonotonic reasoning - LIN, SHOHAM - 1989 |

32 |
Autoepistemic logic and formalization of commonsense reasoning
- Gelfond
- 1989
(Show Context)
Citation Context ...211. Notes 1. The idea of providing for the incompleteness of information in logicbased query answering systems, and permitting answers other than simply yes or no for ground queries, is discussed in =-=[Gelfond1989] and [Gelfond and Li-=-fschitz1990]. Our use of two kinds of negation appears to be somewhat similar to the distinction between "strong" and "weak" negation in [Wagner1989]. 2. Notice for comparison that... |

28 |
Between circumscription and autoepistemic logic
- Lifschitz
- 1989
(Show Context)
Citation Context ...gic is described in [Bidoit and Froidevaux1987] (see also [Lin and Shoham1989]) and shown to be equivalent to stable models in [Bidoit and Froidevaux1988]. Introspective circumscription is defined in =-=[Lifschitz1989]-=-, and its relation to stable models is discussed in Sections 5.1 and 5.2 of that paper. 6. The use of autoepistemic logic for this purpose leads to some complications. They are related to the fact tha... |

19 | Argument systems: A uniform basis for nonmonotonic reasoning - Lin, Shoham - 1989 |

15 |
Three-valued formalizations of non-monotonic reasoning and logic programming
- Przymusinski
- 1989
(Show Context)
Citation Context ... We will return to this point in the next section, and then again in Section 6. We think of answer sets as incomplete theories (rather than "threevalued models," used, for instance, in [Fitt=-=ing1985], [Przymusinski1989]-=- and [Van Gelder et al.1990]). When a program has several answer sets, it is incomplete also in another sense---it has several different interpretations, and the answer to a query may depend on the in... |

14 | and Miroslaw Truszczynski. Autoepistemic logic, defaults and truth maintenance - Marek - 1989 |

13 |
On the relationship between logic programming and non-monotonic reasoning
- Przymusinski
- 1988
(Show Context)
Citation Context ...hardly brings any new computational difficulties. 2 The class of extended programs is of interest in connection with the problem of relation between logic programming and nonmonotonic formalisms (see =-=[Przymusinski1988]-=- for an overview). As shown in [Bidoit and Froidevaux1987], general logic programs can be viewed as default theories in the sense of Reiter [rei80]. A similar reduction is applicable to extended progr... |

11 |
The treatment of negation in logic programs for representing legislation
- Kowalski
- 1989
(Show Context)
Citation Context ... SRI, a more restricted rule should be used instead: :Employed(x; Stanford) / not; Employed(x; Stanford): The following example of the use of negation in the 1981 British Nationality Act is quoted in =-=[Kowalski1989]: "Af-=-ter commencement no person shall have the status of a Commonwealth citizen or the status of a British subject otherwise than under this Act." This statement, in essense, postulates the closed wor... |

11 | Gracefully adding negation and disjunction to prolog - Poole, Goebel - 1986 |

8 | Negation by default and nonstratifiable logic programs - Bidoit, Froidevaux - 1988 |

2 | and Miroslaw Truszczy'nski. Relating autoepistemic and default logic - Marek - 1989 |

1 |
The two sources of nonmonotonicity in vivid logic: weak falsity and inconsistency handling
- Wagner
- 1989
(Show Context)
Citation Context ...ound queries, is discussed in [Gelfond1989] and [Gelfond and Lifschitz1990]. Our use of two kinds of negation appears to be somewhat similar to the distinction between "strong" and "wea=-=k" negation in [Wagner1989]-=-. 2. Notice for comparison that when Poole and Goebel [poo86] add classical negation to Prolog, they immediately get full first order logic and full resolution. This is because they interpret / as cla... |

1 | Negation by default and nonstrati logic programs - Bidoit, Froidevaux - 1988 |