## Specification of Nonmonotonic Reasoning

Venue: | JOURNAL OF APPLIED NON-CLASSICAL LOGICS |

Citations: | 15 - 10 self |

### BibTeX

@INPROCEEDINGS{Engelfriet_specificationof,

author = {Joeri Engelfriet and Jan Treur},

title = {Specification of Nonmonotonic Reasoning},

booktitle = {JOURNAL OF APPLIED NON-CLASSICAL LOGICS},

year = {},

pages = {111--125},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Two levels of description of nonmonotonic reasoning are distinguished. For these levels semantical formalizations are given. The first level is defined semantically by the notion of belief state frame, the second level by the notion of reasoning frame. We introduce two specification languages to describe nonmonotonic reasoning at each of the levels: (1) a specification language for level 1, with formal semantics based on belief state frames, (2) a fragment of infinitary temporal logic as a general specification language for level 2, with formal semantics based on reasoning frames. In our framework every level 2 description can be abstracted to level 1, and for every level 1 description there are level 2 descriptions which are a specialization of it.

### Citations

1423 |
A Logic for Default Reasoning
- Reiter
- 1980
(Show Context)
Citation Context ...rs approaches such as preferential semantics (cf. [Sho87]) and the notion of Sexpansions for modal nonmonotonic logics (cf. [MT93]). The second type at least covers approaches like default logic (cf. =-=[Rei80]-=-). The general specification framework (and its semantics) introduced here provides a unifying perspective on these and other well-known approaches. For example, the general connections between the tw... |

540 | Nonmonotonic reasoning, preferential models and cumulative logics
- Kraus, Lehmann, et al.
- 1990
(Show Context)
Citation Context ...bach (eds.), Practical Reasoning, Proceedings International Conference on Formal and Applied Practical Reasoning, FAPR'96, Lecture Notes in Artificial Intelligence 1085, Springer-Verlag, pp. 111-125. =-=[KLM90]-=-. A disadvantage of this (sceptical) approach may be that hypothetical conclusions that are possible within one of the belief sets may be lost due to the restriction to the common beliefs. So, the age... |

185 | Theoretical Foundations for Non-monotonic Reasoning - Gabbay - 1985 |

148 | General patterns in nonmonotonic reasoning - Makinson - 1994 |

115 | General theory of cumulative inference - Makinson - 1989 |

103 | Multi-Agent Systems: A Theoretical Framework for Intentions - Singh - 1994 |

93 | Reasoning situated in time I: Basic concepts - Elgot-Drapkin, Perlis - 1990 |

88 |
Nonmonotonic logics: meaning and utility
- Shoham
- 1987
(Show Context)
Citation Context ...are the intended outcomes, or at the level of reasoning patterns to construct these outcomes (or both). The first type of specifications at least covers approaches such as preferential semantics (cf. =-=[Sho87]-=-) and the notion of Sexpansions for modal nonmonotonic logics (cf. [MT93]). The second type at least covers approaches like default logic (cf. [Rei80]). The general specification framework (and its se... |

64 |
Nonmonotonic Logics
- Marek, TruszczyĆski
- 1993
(Show Context)
Citation Context ...uct these outcomes (or both). The first type of specifications at least covers approaches such as preferential semantics (cf. [Sho87]) and the notion of Sexpansions for modal nonmonotonic logics (cf. =-=[MT93]-=-). The second type at least covers approaches like default logic (cf. [Rei80]). The general specification framework (and its semantics) introduced here provides a unifying perspective on these and oth... |

52 | On the formal specification and verification of multi-agent systems - Fisher, Wooldridge - 1997 |

49 | Nonmonotonic temporal reasoning - Sandewall, Shoham - 1994 |

34 | Temporal Theories of Reasoning
- Engelfriet, Treur
- 1994
(Show Context)
Citation Context ...and reasoning frames, it means we would also have to adapt the specification languages (for instance by allowing a more general form of formulae, or by dropping the conservativity axioms). In [ET93], =-=[ET94]-=- it is shown for a number of examples how the language of temporal logic can be used to specify sets of intended reasoning patterns. The dualism between multiple outcomes and multiple reasoning traces... |

26 | Compositional Verification of Multi-Agent Systems in Temporal Multi-Epistemic Logic - Engelfriet, Jonker, et al. - 2002 |

23 |
A semantics for default logic
- Etherington
- 1987
(Show Context)
Citation Context ...e and other well-known approaches. For example, the general connections between the two levels developed in the current paper provide connections between preferential semantics and default logic (cf. =-=[Eth87]-=-, [Voo93]) as a special case. Apart from the two levels of abstraction considered here, [EHT95] distinguishes three more levels of abstraction. Sections 2, 3 and 4 review and extend some of the materi... |

21 | A temporal model theory for default logic
- Engelfriet, Treur
- 1993
(Show Context)
Citation Context ...nd if the truth of an infinite conjunction in such a model is decidable (this may depend on the theory of reasoning). For the example of default logic a temporal translation was already introduced in =-=[ET93]. Here a d-=-efault rule ( : ") /' is translated into the temporal rule CsFs"sG', which indeed is a reasoning formula in the sense defined above (notice that translated default rules form a strict subset... |

17 | Representation theory for default logic
- Marek, Treur, et al.
- 1997
(Show Context)
Citation Context ...econditions " (the formulae in B should not be known initially in order for the rule to be applicable), and the set C is a kind of consistency check (as is also used in default logic). Examples a=-=s in [MTT96]-=- show that sometimes we really need an infinite C. Definition 5.2 Let SB = (L, Mod, , ) be a belief state frame. Then the belief state frame specification S SB is defined by the following set of belie... |

14 |
Preference-based Semantics for Nonmonotonic Logics
- Voorbraak
- 1993
(Show Context)
Citation Context ...er well-known approaches. For example, the general connections between the two levels developed in the current paper provide connections between preferential semantics and default logic (cf. [Eth87], =-=[Voo93]-=-) as a special case. Apart from the two levels of abstraction considered here, [EHT95] distinguishes three more levels of abstraction. Sections 2, 3 and 4 review and extend some of the material presen... |

14 | Rules as actions: A situation calculus semantics for logic programs - Lin, Reiter - 1997 |

8 | Compactness properties of nonmonotonic inference operations - Herre - 1994 |

7 |
Minimal Temporal Epistemic Logic
- Engelfriet
- 1995
(Show Context)
Citation Context ... in a way analogous to for instance in [KLM90] (see [EHT95]). Also specification of reasoning can be done in a unified way. Logical properties of the specification language for level 2 are studied in =-=[En95]-=-. Although many nonmonotonic formalisms can be described and specified in our framework, we cannot claim that any reasoning process falls in its scope. We would like to relax some of the conditions fo... |

7 | Default Logic and Specification of Nonmonotonic Reasoning - Engelfriet, Marek, et al. - 2001 |

6 | Nonmonotonic Belief State Frames and Reasoning Frames (extended abstract
- Engelfriet, Herre, et al.
- 1995
(Show Context)
Citation Context ...developed in the current paper provide connections between preferential semantics and default logic (cf. [Eth87], [Voo93]) as a special case. Apart from the two levels of abstraction considered here, =-=[EHT95]-=- distinguishes three more levels of abstraction. Sections 2, 3 and 4 review and extend some of the material presented there. 2 Belief state frames Classical (propositional) logic lies at the basis of ... |

3 | Magidor: "Nonmonotonic Reasoning, Preferential models and cumulative logics - Kraus, Lehmann, et al. - 1990 |

1 | Minimal Temporal Epistemic Logic", Notre Dame - Engelfriet - 1996 |