## On the Semantics of Theory Change: Arbitration between Old and New Information (1993)

Venue: | In Proceedings of the Twelfth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases |

Citations: | 54 - 0 self |

### BibTeX

@INPROCEEDINGS{Revesz93onthe,

author = {Peter Z. Revesz},

title = {On the Semantics of Theory Change: Arbitration between Old and New Information},

booktitle = {In Proceedings of the Twelfth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases},

year = {1993},

pages = {71--82}

}

### Years of Citing Articles

### OpenURL

### Abstract

: Katsuno and Mendelzon divide theory change, the problem of adding new information to a logical theory, into two types: revision and update. We propose a third type of theory change: arbitration. The key idea is the following: the new information is considered neither better nor worse than the old information represented by the logical theory. The new information is simply one voice against a set of others already incorporated into the logical theory. From this follows that arbitration should be commutative. First we define arbitration by a set of postulates and then describe a model-theoretic characterization of arbitration for the case of propositional logical theories. We also study weighted arbitration where different models of a theory can have different weights. 1 Introduction The problem of updating logical theories is a common fundamental concern to databases, to Artificial Intelligence [McC68, Rei92], and to belief revision [Mak85, Gar88]. It is well-known that giving semant...

### Citations

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(Show Context)
Citation Context ...FUV83], Grahne, Mendelzon and Revesz [GMR92], Satoh [Sat88], Weber [Web86], and Winslett [Win88]. Taking the second direction, sets of postulates were proposed by Alchourr'on, Gardenfors and Makinson =-=[AGM85]-=- and by Katsuno and Mendelzon [KM91]. Katsuno and Mendelzon point out that there are no universally desirable set of postulates. In particular they argue that the AGM postulates describe one type of t... |

612 |
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Citation Context ...onotone. That is, for any update operator if OE implies /, then OE \Pi �� implies / \Pi ��. However, Gardenfors' impossibility theorem shows that no non-trivial revision operator can be monoto=-=ne (see [Gar88]-=- for the result and the logical definition of non-trivial). From these it follows that the set of non-trivial revision and the set of update operators are disjoint. This result can be strengthened by ... |

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Citation Context ...o formulas, not to models. They are also different from the weights of Dalal [Dal88] which are assigned to propositions. They also have only vague connection with probabilities and possibility values =-=[Zad78]-=- which both have a constant one as an upper bound, unlike weights. The research described here has much practical relevance to databases. We believe that the three types of theory change operations co... |

402 | On the difference between updating a knowledge base and revising it
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Citation Context ...[GMR92], Satoh [Sat88], Weber [Web86], and Winslett [Win88]. Taking the second direction, sets of postulates were proposed by Alchourr'on, Gardenfors and Makinson [AGM85] and by Katsuno and Mendelzon =-=[KM91]-=-. Katsuno and Mendelzon point out that there are no universally desirable set of postulates. In particular they argue that the AGM postulates describe one type of theory change --revision-- while the ... |

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Citation Context ...[GMR92], Satoh [Sat88], Weber [Web86], and Winslett [Win88]. Taking the second direction, sets of postulates were proposed by Alchourr'on, Gardenfors and Makinson [AGM85] and by Katsuno and Mendelzon =-=[KM91]-=-. Katsuno and Mendelzon point out that there are no universally desirable set of postulates. In particular they argue that the AGM postulates describe one type of theory change --revision-- while the ... |

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Citation Context ...e first direction concrete operators were proposed by Borgida [Bor85], Dalal [Dal88], Fagin, Ullman and Vardi [FUV83], Grahne, Mendelzon and Revesz [GMR92], Satoh [Sat88], Weber [Web86], and Winslett =-=[Win88]-=-. Taking the second direction, sets of postulates were proposed by Alchourr'on, Gardenfors and Makinson [AGM85] and by Katsuno and Mendelzon [KM91]. Katsuno and Mendelzon point out that there are no u... |

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Citation Context ...by giving a set of axioms or postulates that every adequate theory change operator should be expected to satisfy. Taking the first direction concrete operators were proposed by Borgida [Bor85], Dalal =-=[Dal88]-=-, Fagin, Ullman and Vardi [FUV83], Grahne, Mendelzon and Revesz [GMR92], Satoh [Sat88], Weber [Web86], and Winslett [Win88]. Taking the second direction, sets of postulates were proposed by Alchourr'o... |

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Citation Context ...ulates that every adequate theory change operator should be expected to satisfy. Taking the first direction concrete operators were proposed by Borgida [Bor85], Dalal [Dal88], Fagin, Ullman and Vardi =-=[FUV83]-=-, Grahne, Mendelzon and Revesz [GMR92], Satoh [Sat88], Weber [Web86], and Winslett [Win88]. Taking the second direction, sets of postulates were proposed by Alchourr'on, Gardenfors and Makinson [AGM85... |

109 | On Closed World databases - Reiter - 1978 |

98 | Language features for flexible handling of exceptions in information systems
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Citation Context ...wer indirectly by giving a set of axioms or postulates that every adequate theory change operator should be expected to satisfy. Taking the first direction concrete operators were proposed by Borgida =-=[Bor85]-=-, Dalal [Dal88], Fagin, Ullman and Vardi [FUV83], Grahne, Mendelzon and Revesz [GMR92], Satoh [Sat88], Weber [Web86], and Winslett [Win88]. Taking the second direction, sets of postulates were propose... |

77 | On specifying database updates - Reiter - 1992 |

63 |
Nonmonotonic Reasoning by Minimal Belief Revision
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Citation Context ...uld be expected to satisfy. Taking the first direction concrete operators were proposed by Borgida [Bor85], Dalal [Dal88], Fagin, Ullman and Vardi [FUV83], Grahne, Mendelzon and Revesz [GMR92], Satoh =-=[Sat88]-=-, Weber [Web86], and Winslett [Win88]. Taking the second direction, sets of postulates were proposed by Alchourr'on, Gardenfors and Makinson [AGM85] and by Katsuno and Mendelzon [KM91]. Katsuno and Me... |

44 |
On the use of an extended relational model to handle changing incomplete information
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Citation Context ...y change --revision-- while the KM postulates describe another --update. An informal distinction between these two types was also made before by Abiteboul and Grahne [AG85] and by Keller and Winslett =-=[KW85]-=-. This paper introduces a third type of theory change -- arbitration-- and shows it to be distinct from both revision and update. The three types of theory change assume quite different relations betw... |

42 | A.O.: A unified view of propositional knowledge base updates - Katsuno, Mendelzon - 1989 |

42 |
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(Show Context)
Citation Context ... to satisfy. Taking the first direction concrete operators were proposed by Borgida [Bor85], Dalal [Dal88], Fagin, Ullman and Vardi [FUV83], Grahne, Mendelzon and Revesz [GMR92], Satoh [Sat88], Weber =-=[Web86]-=-, and Winslett [Win88]. Taking the second direction, sets of postulates were proposed by Alchourr'on, Gardenfors and Makinson [AGM85] and by Katsuno and Mendelzon [KM91]. Katsuno and Mendelzon point o... |

41 | How to give it up: a survey of some formal aspects of the logic of theory change - Makinson - 1985 |

37 | Non-deterministic languages to express deterministic transformations - Abiteboul, Simon, et al. - 1992 |

34 |
Update semantics for incomplete databases, in
- Abiteboul, Grahne
- 1985
(Show Context)
Citation Context ...tulates describe one type of theory change --revision-- while the KM postulates describe another --update. An informal distinction between these two types was also made before by Abiteboul and Grahne =-=[AG85]-=- and by Keller and Winslett [KW85]. This paper introduces a third type of theory change -- arbitration-- and shows it to be distinct from both revision and update. The three types of theory change ass... |

14 | Knowledgebase Transformations
- Grahne, Mendelzon, et al.
- 1997
(Show Context)
Citation Context ...85, Gar88]. It is well-known that giving semantics to updates is difficult once the logical theory is complex enough to express views or integrity constraints [BS81, FUV83]. For a simple example from =-=[GMR92]-=- consider the propositional database represented by the theory fA; B; AsB ! Cg. If we want to add the inPart of the research presented here was done while the author was a postdoctoral fellow at the U... |

12 |
and A Mendelzon. On the difference between updating a knowledgebase and revising it. Belief Revision
- Katsuno
- 1992
(Show Context)
Citation Context ...ch knowledge-base / to a total pre-orders/ such that Mod(/ 4 OE) = Min(M; /OE ). 2 An interesting question is whether the three types of theory change operators are disjoint. As Katsuno and Mendelzon =-=[KM92] point o-=-ut all update operators are monotone. That is, for any update operator if OE implies /, then OE \Pi �� implies / \Pi ��. However, Gardenfors' impossibility theorem shows that no non-trivial re... |