Nonmonotonic Reasoning with Multiple Belief Sets

J. Engelfriet; H. Herre; J. Treur

doi:10.1007/3-540-61313-7_83

Nonmonotonic Reasoning with Multiple Belief Sets

J. Engelfriet, H. Herre, J. Treur

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

Abstract

In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze multiple belief sets in an abstract setting. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selective inference operations connected to belief set operators and which are used to choose one of the possible views.

Original language	English
Title of host publication	Practical Reasoning - International Conference on Formal and Applied Practical Reasoning, FAPR 1996, Proceedings
Publisher	Springer/Verlag
Pages	331-344
Number of pages	15
Volume	1085
ISBN (Print)	3540613137, 9783540613138
DOIs	https://doi.org/10.1007/3-540-61313-7_83
Publication status	Published - 1996
Event	International Conference on Formal and Applied Practical Reasoning, FAPR 1996 - Bonn, Germany Duration: 3 Jun 1996 → 7 Jun 1996

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher	Springer
Volume	1085
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Conference on Formal and Applied Practical Reasoning, FAPR 1996
Country	Germany
City	Bonn
Period	3/06/96 → 7/06/96

Keywords

Belief sets
Knowledge representation
Nonmonotonic inference

Access to Document

10.1007/3-540-61313-7_83

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Cite this

Engelfriet, J., Herre, H., & Treur, J. (1996). Nonmonotonic Reasoning with Multiple Belief Sets. In Practical Reasoning - International Conference on Formal and Applied Practical Reasoning, FAPR 1996, Proceedings (Vol. 1085, pp. 331-344). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1085). Springer/Verlag. https://doi.org/10.1007/3-540-61313-7_83

Engelfriet, J. ; Herre, H. ; Treur, J. / Nonmonotonic Reasoning with Multiple Belief Sets. Practical Reasoning - International Conference on Formal and Applied Practical Reasoning, FAPR 1996, Proceedings. Vol. 1085 Springer/Verlag, 1996. pp. 331-344 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze multiple belief sets in an abstract setting. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selective inference operations connected to belief set operators and which are used to choose one of the possible views.",

keywords = "Belief sets, Knowledge representation, Nonmonotonic inference",

author = "J. Engelfriet and H. Herre and J. Treur",

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booktitle = "Practical Reasoning - International Conference on Formal and Applied Practical Reasoning, FAPR 1996, Proceedings",

note = "International Conference on Formal and Applied Practical Reasoning, FAPR 1996 ; Conference date: 03-06-1996 Through 07-06-1996",

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Engelfriet, J, Herre, H & Treur, J 1996, Nonmonotonic Reasoning with Multiple Belief Sets. in Practical Reasoning - International Conference on Formal and Applied Practical Reasoning, FAPR 1996, Proceedings. vol. 1085, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1085, Springer/Verlag, pp. 331-344, International Conference on Formal and Applied Practical Reasoning, FAPR 1996, Bonn, Germany, 3/06/96. https://doi.org/10.1007/3-540-61313-7_83

Nonmonotonic Reasoning with Multiple Belief Sets. / Engelfriet, J.; Herre, H.; Treur, J.

Practical Reasoning - International Conference on Formal and Applied Practical Reasoning, FAPR 1996, Proceedings. Vol. 1085 Springer/Verlag, 1996. p. 331-344 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1085).

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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AB - In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze multiple belief sets in an abstract setting. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selective inference operations connected to belief set operators and which are used to choose one of the possible views.

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Engelfriet J, Herre H, Treur J. Nonmonotonic Reasoning with Multiple Belief Sets. In Practical Reasoning - International Conference on Formal and Applied Practical Reasoning, FAPR 1996, Proceedings. Vol. 1085. Springer/Verlag. 1996. p. 331-344. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-61313-7_83