## Logic Programming and Reasoning with Incomplete Information (1994)

Venue: | Annals of Mathematics and Artificial Intelligence |

Citations: | 38 - 4 self |

### BibTeX

@ARTICLE{Gelfond94logicprogramming,

author = {Michael Gelfond},

title = {Logic Programming and Reasoning with Incomplete Information},

journal = {Annals of Mathematics and Artificial Intelligence},

year = {1994},

volume = {12}

}

### OpenURL

### Abstract

The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and negation by failure is further expanded by new modal operators K and M (where for the set of rules T and formula F , KF stands for "F is known to be true by a reasoner with a set of premises T " and MF means " F may be believed to be true" by the same reasoner). Sets of rules in the extended language will be called epistemic specifications. We will define the semantics of epistemic specifications (which expands the semantics of disjunctive databases from [GL91]) and demonstrate their applicability to formalization of various forms of commonsense reasoning. In particular, we suggest a new formalization of the closed world assumption which seems to better correspond to the assumption's intuitive...

### Citations

1550 | The stable model semantics for logic programming
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- 1988
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Citation Context ...s, or belief sets) consist of literals and therefore are vivid in the sense of H. Levesque [Lev86]. For extended programs without classical negation their answer sets coincide with stable models from =-=[GL88]-=-. In [GL90] we consider primarily well-defined extended logic programs, i.e. extended programs with unique consistent answer sets. The answer such a program returns to a ground query Q 2 is yes, no, o... |

1473 |
A logic for default reasoning
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977 |
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260 |
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234 |
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- 1980
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Citation Context ...ng will be used to provide a specification of a reasoner with the desired beliefs. (This view on the role of logic in nonmonotonic reasoning seems to be similar to the one advocated by H. Levesque in =-=[Lev90]-=-). Formally, by an epistemic specification we will mean a collection of rules of the form F / G 1 ; : : : ; Gm ; not Gm+1 ; : : : ; not G k (3) where F and Gm+1 : : : G k are objective and G 1 : : : G... |

187 | Foundations of Disjunctive Logic Programming
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Citation Context ...ited since their semantics suggested in [Min82] implicitly assumes a form of closed world assumption. This work was generalized and/or modified by various authors (an overview can be found in [PP90], =-=[LMR92]-=-) but most of the approaches still assume the closed world assumption and hence does not allow the representation of such simple forms of incompleteness as missing informations in the database tables,... |

180 |
Making Prolog more expressive
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Citation Context ...ghGPA(Mike) HighGPA(Mike) / not FairGPA(Mike) will not change answer sets of the program. In this paper we extend the syntax of disjunctive databases from [GL91] in two directions. Firstly, following =-=[LT84]-=-, and [Wag91] we allow the rules to contain other types of formulae in addition to literals. Secondly, and more importantly, we expand the language by a modal operators K and M. Sets of rules in the e... |

111 |
On Stratified Autoepistemic Theories
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Citation Context ...ave a reasonably good understanding of the relationship between these formalisms and special classes of epistemic specifications. For the equivalence results about various subclasses see for instance =-=[Gel87]-=-, [BF87], [GLPT91]. It is more difficult to use these formalisms to model modal operators of epistemic specifications. Autoepistemic logics, which seem to be natural candidates for such modeling, appa... |

102 |
Making believers out of computers
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96 |
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Citation Context ...P . Such a multiplicity becomes a norm rather than exception if the notion of extended logic program and its answer set semantics is expanded to that of extended disjunctive database [GL91] (see also =-=[Prz90] ) --- col-=-lections of rules of the form: A 1 or : : : or A n / B 1 ; :::; Bm ; not C 1 ; : : : ; not C k (2) where A's, B's, and C's are atoms p or their "classical" negations :p. We will assume that ... |

83 |
Logic Programs with Exceptions
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Citation Context ...unctive databases and differ from that of . The meaning of a formula AsB is "A is true or B is true" while a rule 1 A similar approach was independently developed and investigated in [PW89].=-= See also [KS90]. 2 Here Q-=- is a literal. In the next section we will consider more complicated queries A or B / is interpreted epistemically and means "A is believed to be true or B is believed to be true.") Let \Del... |

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Citation Context ...ble sentences, which represent the incompleteness of information in classical axiomatic theories. The first attempt to lift the syntactic limitation described above is probably due to Jack Minker. In =-=[Min82]-=- he considers positive disjunctive databases defined as collections of rules of the form A 1 or : : : or A n / B 1 ; :::; Bm (1) where A 0 s and B 0 s are atoms. The type of incompleteness expressible... |

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48 |
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41 | Possible Model Semantics for Disjunctive Databases - Sakama - 1989 |

31 |
Modal logic for default reasoning
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- 1990
(Show Context)
Citation Context ...4 Appendix In this section we will brie y discuss the relationship between epistemic speci cations and some other general purpose nonmonotonic formalisms such as autoepistemic logics [MD80], [Moo85], =-=[MT90]-=-, and default logic of R. Reiter [Rei80] and its extension [GLPT91]. By now wehave a reasonably good understanding of the relationship between these formalisms and special classes of epistemic speci c... |

28 | Hypothetical reasoning with well founded semantics
- Pereira, Aparı́cio, et al.
- 1991
(Show Context)
Citation Context ... This coding can be viewed as a combination of the representation of normative statements in circumscription with the method used in non-monotonic modal logics [McC80, MD80]. It was also advocated in =-=[PCA91]. For-=- illustration, let us consider database T 1 from Example 10 and expand it by the following information: "As a rule, professors in the computer science department have vax accounts. This rule is n... |

22 |
and Halina Przymusinska. Negation as failure: careful closure procedure
- Gelfond
- 1986
(Show Context)
Citation Context ...: : : or A n / B 1 ; : : : ; Bm (6) by a formula B 1 & : : : &Bm oe A 1s: : :sA n (7) Recall that Minker's generalized closed world assumption is defined as follows. (We will use the terminology from =-=[GP86]-=-.) A disjunction D of ground atoms is called essential w.r.t. theory \Pi if \Pi j= D and no subdisjunction of D is entailed by \Pi. A ground atom is called free for negation in \Pi if it does not belo... |

22 |
On asking what a database knows
- Reiter
- 1990
(Show Context)
Citation Context ...accepted interpretation of the meaning and the role of integrity constraints in knowledge representation. In this paper we will adopt the view on integrity constraints recently suggested by Reiter in =-=[Rei90]-=-. According to Reiter an integrity constraint IC is a statement about the content of the knowledge base T (as opposed to IC being a statement about the world). T satisfies IC iff the answer to IC when... |

19 |
Strong introspection
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- 1991
(Show Context)
Citation Context ...swer to this question is undetermined, and, by (*), Mike should be interviewed. To formalize this argument our system should have a more powerful introspective ability (termed strong introspection in =-=[Gel91]-=-) than the one captured by the notion of answer sets from [GL91]. Roughly speaking instead of looking at only one possible set of beliefs sanctioned by T it should be able to look at all such sets. Re... |

9 |
Halina Przymusi'nska, and Miros/law Truszczy'nski. Disjunctive defaults
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Citation Context ... between epistemic specifications and some other general purpose nonmonotonic formalisms such as autoepistemic logics [MD80], [Moo85], [MT90], and default logic of R. Reiter [Rei80] and its extension =-=[GLPT91]-=-. By now we have a reasonably good understanding of the relationship between these formalisms and special classes of epistemic specifications. For the equivalence results about various subclasses see ... |

9 |
Reasoning with negative information 1 -- strong negation in logic programming
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- 1989
(Show Context)
Citation Context ...semantics of disjunctive databases and differ from that of . The meaning of a formula AsB is "A is true or B is true" while a rule 1 A similar approach was independently developed and invest=-=igated in [PW89]. See-=- also [KS90]. 2 Here Q is a literal. In the next section we will consider more complicated queries A or B / is interpreted epistemically and means "A is believed to be true or B is believed to be... |

8 | The extended closed world assumption and its relation to parallel circumscription - Gelfond, Przymusinska, et al. - 1986 |

6 |
WF3 : A Semantics for Negation in Normal Disjunctive Logic Programs with Equivalent Proof Methods
- Baral, Lobo, et al.
- 1991
(Show Context)
Citation Context ...r simple queries about their knowledge of the world. The next example demonstrates how they can answer more complicated queries. The following story was discussed (in a somewhat different context) in =-=[BLM91]-=-. Example 11. Assume that we are preparing for a camping trip and we are deciding what equipment we are going to take on the trip. We would like to bring with us a stove and a blanket. However, we hav... |

4 |
A Possible World Semantics for Non-Horn Databases
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- 1989
(Show Context)
Citation Context ... closed world assumption which differs from the other proposals and will discuss the suitability of this assumption for knowledge representation. We will start with the following example: Example 10. =-=[Cha89]. Sup-=-pose we are given the following information: (*) "If a suspect is violent and is a psychopath then the suspect is extremely dangerous. This is not the case if the suspect is not violent or not a ... |

4 |
and Miros/law Truszczy'nski. Modal logic for default reasoning
- Marek
- 1990
(Show Context)
Citation Context ...Appendix In this section we will briefly discuss the relationship between epistemic specifications and some other general purpose nonmonotonic formalisms such as autoepistemic logics [MD80], [Moo85], =-=[MT90]-=-, and default logic of R. Reiter [Rei80] and its extension [GLPT91]. By now we have a reasonably good understanding of the relationship between these formalisms and special classes of epistemic specif... |

4 |
On strati ed autoepistemic theories
- Gelfond
- 1987
(Show Context)
Citation Context ...have a reasonably good understanding of the relationship between these formalisms and special classes of epistemic speci cations. For the equivalence results about various subclasses see for instance =-=[Gel87]-=-, [BF87], [GLPT91]. It is more di cult to use these formalisms to model modal operators of epistemic speci cations. Autoepistemic logics, which seem to be natural candidates for such modeling, apparen... |

3 |
and Halina Przymusi'nska. Definitions in epistemic specifications
- Gelfond
- 1991
(Show Context)
Citation Context ...ilar problem arises when default logic is used for the same purpose. A more detailed discussion of this (as well as some ideas about computing world views of epistemic specifications) can be found in =-=[GP91]-=-. Acknowledgments I would like to thank Vladimir Lifschitz, Halina Przymusinska, Marek Suchenek, Bonnie Traylor and Thomas Woo for suggestions on a draft of this paper. Special thanks to Teodor Przymu... |

1 |
and Halina Przymusinska. De nitions in epistemic speci cations
- Gelfond
- 1991
(Show Context)
Citation Context ...milar problem arises when default logic is used for the same purpose. A more detailed discussion of this (as well as some ideas about computing world views of epistemic speci cations) can be found in =-=[GP91]-=-. Acknowledgments Iwould like to thank Vladimir Lifschitz, Halina Przymusinska, Marek Suchenek, Bonnie Traylor and Thomas Woo for suggestions on a draft of this paper. Special thanks to Teodor Przymus... |

1 |
On inde nite data bases and the closed world assumption
- Minker
- 1982
(Show Context)
Citation Context ...dable sentences, which represent the incompleteness of information in classical axiomatic theories. The rst attempt to lift the syntactic limitation described above is probably due to Jack Minker. In =-=[Min82]-=- he considers positive disjunctive databases de ned as collections of rules of the form A1 or ::: or An B1� :::� Bm (1) where A 0 s and B 0 s are atoms. The type of incompleteness expressible in these... |