## Reasoning in Open Domains (1993)

Venue: | In Logic Programming and Non-Monotonic Reasoning |

Citations: | 19 - 1 self |

### BibTeX

@INPROCEEDINGS{Gelfond93reasoningin,

author = {Michael Gelfond and Halina Przymusinska},

title = {Reasoning in Open Domains},

booktitle = {In Logic Programming and Non-Monotonic Reasoning},

year = {1993},

pages = {397--413},

publisher = {MIT Press}

}

### OpenURL

### Abstract

In this paper we modify the semantics of epistemic specifications (and hence the answer set semantics of extended logic program and disjunctive databases) to allow for reasoning in the absence of domain--closure assumption. This modification increases the expressive power of the language and allows one to explicitly state the domain--closure and other assumptions about the domain of discourse in the language of epistemic specifications. The power of the language is demonstrated by way of examples. In particular we show how open domain assumption can be used to formalize default reasoning in the presence of anonymous exceptions to defaults. 1 Introduction Epistemic specifications were introduced in [4] as a tool for knowledge representation. They can be viewed as a generalization of "extended disjunctive databases" from [6] capable of expressing powerful forms of introspection. The semantics of an epistemic specification 5 has been given via the notion of a world view of 5 - a collect...

### Citations

884 | Classical negation in logic programs and disjunctive databases. New Generation Computing 9:365–385
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...ons to defaults. 1 Introduction Epistemic specifications were introduced in [4] as a tool for knowledge representation. They can be viewed as a generalization of "extended disjunctive databases&q=-=uot; from [6]-=- capable of expressing powerful forms of introspection. The semantics of an epistemic specification 5 has been given via the notion of a world view of 5 - a collection of vivid theories about the worl... |

736 | The semantics of predicate logic as a programming language
- Emden, Kowalski
- 1976
(Show Context)
Citation Context ...e from the literature: Example 8. Consider a positive logic program: Pa / and a query Q = 8xPx. Under the domain--closure assumption the semantics of this program is given by its least Herbrand model =-=[1]-=-, and hence 5's answer to a query Q will be yes. However, if we add to 5 an apparently unrelated fact Rb, the answer of the new program 5 3 to the same query Q becomes no. This lack of modularity, the... |

508 | Applications of circumscription to formalizing common-sense reasoning
- McCarthy
- 1986
(Show Context)
Citation Context ...ocess. It may be interesting to look for classes of specifications and/or queries for which E 5 is redundant. 3.3 Anonymous exceptions to defaults Let us now consider a classical flying birds example =-=[10]-=-, in which we are told that penguins are birds that do not fly, that birds normally fly, and that Tweety is a bird. The example served as a testing ground for various nonmonotonic formalisms. Many for... |

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

284 |
On Closed World Data Bases
- Reiter
- 1978
(Show Context)
Citation Context ...d p stands for prof . This allows us to conclude, say, that a is not a professor without concluding that there are no professors except m and n. 3.2 Unique name assumption. The unique name assumption =-=[12]-=- is normally used in settings when one can assume that all the relevant information about the equality of individuals has been specified. In this case all pairs of individuals not specified as identic... |

104 |
Making Believers out of computers
- Levesque
- 1986
(Show Context)
Citation Context ...apable of expressing powerful forms of introspection. The semantics of an epistemic specification 5 has been given via the notion of a world view of 5 - a collection of vivid theories about the world =-=[8]-=- which can be built by a rational reasoner on the instructions from 5. The concept of a world view of 5 was defined in two steps: first the rules from 5 were replaced by their ground instances, and th... |

64 | On the declarative and procedural semantics of logic programs
- Przymusinski
- 1995
(Show Context)
Citation Context ...erbrand) minimal models. This allows us to avoid the universal query problem -- under proper definition of an answer to a query both 5 and 5 3 answer unknown to Q. At the same time the semantics from =-=[11]-=- do not diverge too far from the least Herbrand model semantics. In fact, these two semantics are equivalent for existential queries [7]. 7 Our paper can be viewed as an extension of the approach from... |

55 | A Procedural Semantics for WellFounded Negation in Logic Programs
- Ross
- 1992
(Show Context)
Citation Context ... logic program 5: 7 T. Przymusinski's approach is not limited to positive programs. In [11] it is extended to perfect model semantics, etc. Another solution of universal query problem is suggested in =-=[14]-=-. It is based on the assumption that the language of any logic program contains infinitely many constants not appearing in it explicitly. Under this semantics, both programs 5 and 5 3 answer no to the... |

42 | On open defaults
- Lifschitz
- 1990
(Show Context)
Citation Context ...ons but at the same time allows us to define a predicate H which, together with the use of the rules with empty heads is the basic tool for formalization of the domain--closure and other assumptions. =-=[9]-=- is another recent paper closely related to the subject of our work. It suggests a variant of Reiter's default logic aimed at formalization of reasoning about domains without domain--closure assumptio... |

37 |
Equality and Domain Closure in First-Order Databases
- Reiter
- 1980
(Show Context)
Citation Context ...as given for specifications not containing variables. Equating a specification 5 with the set of its ground instances which occurs during the first step was justified by the domain closure assumption =-=[13]-=- which asserts that all objects in the domain of discourse have names in the language of 5. Even though the assumption is undoubtedly useful for a broad range of applications there are cases when it d... |

25 | Nonmonotonicity and the Scope of Reasoning
- Etherington, Kraus, et al.
- 1991
(Show Context)
Citation Context ...s, and closed world assumptions. As another example of applicability of the new semantics to knowledge representation we discuss a possible solution to the problem of anonymous extensions to defaults =-=[2]-=-. Readers who wish to ignore global introspection and restrict their reading to extended logic programs can do so by examining the first two steps of the definition in section two and replacing all oc... |

19 |
Strong introspection
- Gelfond
- 1991
(Show Context)
Citation Context ...articular we show how open domain assumption can be used to formalize default reasoning in the presence of anonymous exceptions to defaults. 1 Introduction Epistemic specifications were introduced in =-=[4] as a tool-=- for knowledge representation. They can be viewed as a generalization of "extended disjunctive databases" from [6] capable of expressing powerful forms of introspection. The semantics of an ... |

10 | On the relationship between CWA, Minimal Model, and Minimal Herbrand Model semantics
- Gelfond, Przymusinska, et al.
- 1990
(Show Context)
Citation Context ...d 5 3 answer unknown to Q. At the same time the semantics from [11] do not diverge too far from the least Herbrand model semantics. In fact, these two semantics are equivalent for existential queries =-=[7]-=-. 7 Our paper can be viewed as an extension of the approach from [11] to epistemic specifications. It is worth noting that even in the language of extended logic programs the presence of classical neg... |

2 |
Epistemic semantics for disjunctive databases
- Gelfond
- 1991
(Show Context)
Citation Context ...ut the equality of individuals has been specified. In this case all pairs of individuals not specified as identical are assumed to be different. To express this assumption we follow the approach from =-=[3]-=- and introduce a new binary predicate symbol E which stands for equality. The specification consisting of the rules (1) -- (5) can be viewed as the definition of E: E 1 : E(x; x) / E 2 : E(x; y) / E(y... |