1457:
437:
Everaere, Konieczny and
Marquis study belief-merging operators in settings in which the different information sources are strategic, and may try to change their stated beliefs in order to influence the outcome. They study strategyproof merging operators.
112:
Konieczny and Perez extended their framework to merging under a set of exogenously imposed constraints that have to be satisfied by the combined database. Their framework is now the standard framework for belief merging. In their framework, a
107:
Combination operators ignore the information about the source of the knowledge bases, so they cannot take into account the number of experts supporting each proposition. In particular, they cannot make decisions based on a majority vote among
451:. To illustrate, suppose three experts support propositions x1,x2,x3,x4 and oppose propositions y1,y2,y3,y4, whereas a fourth expert opposes propositions x1,x2,x3,x4 and supports propositions y1,y2,y3,y4. Then:
458:
The egalitarian rule (minimizing the maximum distances) will choose x1,x2,y1,y2; this is unfair to the majority experts, who are represented by only 2 out of 4 propositions, even though they are 3/4 of the
395:
Konieczny, Lang and
Marquis present the DA framework, which generalizes the merging framework. They prove that, in this framework, query entailment from merged bases is only at the first level of the
64:
approach, we take the union of the knowledge bases (a finite set of logical formulas). If the union is consistent, we are done. Otherwise, we select some maximal consistent subset of it. Baral,
514:- a similar term but refers to a different process, in which the beliefs are expressed as probability distributions over events, and the goal is to aggregate them into a single distribution.
104:
Combination is syntax-dependent, whereas merging is based on the principle of irrelevance of syntax: an operation on two equivalent databases should return two equivalent databases.
88:
approach, the assumption is that all sources of information (both old and new) are equally reliable, so the resulting base should contain as much as possible of both sources.
495:- a closely-related process, in which several experts express their own judgement (as a logical formula), and society has to aggregate them in a consistent way.
411:, in which opinions of different citizens have to be combined into a single "social" opinion. Meyer, Ghose and Chopra relate belief-merging to social choice,
455:
The utilitarian rule (minimizing the sum of distances) will choose x1,x2,x3,x4; this is unfair to the minority expert, who is not represented at all.
508:- a closely-related process, in which an individual changes an existing knowledge base after receiving a new and conflicting piece of information.
1391:
1349:
1273:
1228:
1093:
909:
751:
549:
441:
Haret and
Wallner show that most aggregation procedures are manipulable, and study the computational complexity of finding a manipulation.
408:
958:"Propositional belief base merging or how to merge beliefs/goals coming from several sources and some links with social choice theory"
427:
100:
approach was presented by
Konieczny and Perez. There are several differences between combination operators and merging operators:
31:, into a consistent knowledge-base. Applications include combining conflicting sensor information received by the same agent (see
423:
1478:
539:
76:, for combining multiple knowledge bases which may have inconsistencies, uncertainties, and nonmonotonic modes of negation.
473:
can be seen as a special case of belief-merging with constraints, where the constraints encode the size of the committee.
463:
412:
1467:
1215:. Lecture Notes in Computer Science. Vol. 11468. Cham: Springer International Publishing. pp. 133–150.
447:
Haret, Lackner, Pfandler and
Wallner study belief-merging operators that satisfy fairness properties, similar to
27:, is a process in which an individual agent aggregates possibly conflicting pieces of information, expressed in
448:
466:, would choose x1,x2,x3,y1, which satisfies "justified representation" for both the minority and the majority.
72:, and to resolve inconsistencies among them.Subrahamanian presents a uniform theoretical framework, based on
1409:"Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation"
875:
Proceedings of the
Seventh International Conference on Principles of Knowledge Representation and Reasoning
736:
Proceedings of the twelfth ACM SIGACT-SIGMOD-SIGART symposium on
Principles of database systems - PODS '93
373:
347:
569:
444:
Haret, Pfandler and
Woltran consider some classic social choice axioms in the context of belief merging.
1004:
492:
126:
1110:
957:
1378:. Lecture Notes in Computer Science. Vol. 3571. Berlin, Heidelberg: Springer. pp. 514–526.
1080:. Lecture Notes in Computer Science. Vol. 2143. Berlin, Heidelberg: Springer. pp. 466–477.
896:. Lecture Notes in Computer Science. Vol. 1638. Berlin, Heidelberg: Springer. pp. 233–244.
396:
482:
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44:
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28:
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68:, Minker and Subrahmanian present algorithms for combining knowledge-bases consisting of
1366:
1290:
1253:
585:
163:
1331:
1289:
Haret, Adrian; Lackner, Martin; Pfandler, Andreas; Wallner, Johannes P. (2020-04-03).
1501:
1238:
870:
517:
388:
40:
32:
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653:
481:
The formal methods developed for belief merging have been applied in other areas of
1193:
855:
808:
761:
1265:
601:
1126:
1049:
1032:
926:
1220:
732:"On the semantics of theory change: Arbitration between old and new information"
65:
1258:
Proceedings of the Twenty-second
European Conference on Artificial Intelligence
973:
731:
1424:
1341:
942:
839:
1432:
1316:
1307:
1185:
1134:
1085:
1058:
981:
901:
847:
800:
716:
645:
593:
568:
Baral, Chitta; Kraus, Sarit; Minker, Jack; Subrahmanian, V. S. (1992-02-01).
1408:
823:
667:
36:
1456:
357:
and the interpretation of the outcome (where "distance" can be measured by
877:. KR'00. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.: 135–144.
743:
738:. New York, NY, USA: Association for Computing Machinery. pp. 71–82.
636:
619:
383:
and the interpretation of the outcome. This corredponds similarly to the
1383:
1209:"Manipulating Skeptical and Credulous Consequences when Merging Beliefs"
342:
They present several operators that satisfy all these properties, e.g.:
151:, representing constraints. It should satisfy the following postulates:
776:
1176:
871:"On the difference between merging knowledge bases and combining them"
792:
1254:"Beyond IC postulates: classification criteria for merging operators"
708:
692:
1372:
Symbolic and
Quantitative Approaches to Reasoning with Uncertainty
1166:
1078:
Symbolic and Quantitative Approaches to Reasoning with Uncertainty
894:
Symbolic and Quantitative Approaches to Reasoning and Uncertainty
1252:
Haret, Adrian; Pfandler, Andreas; Woltran, Stefan (2016-08-29).
1365:
Gauwin, Olivier; Konieczny, SĂ©bastien; Marquis, Pierre (2005).
538:
Elmagarmid, Ahmed K.; Rusinkiewicz, Marek; Sheth, Amit (1999).
1450:
1211:. In Calimeri, Francesco; Leone, Nicola; Manna, Marco (eds.).
1111:"Social choice theory, belief merging, and strategy-proofness"
570:"COMBINING KNOWLEDGE BASES CONSISTING OF FIRST-ORDER THEORIES"
1295:
Proceedings of the AAAI Conference on Artificial Intelligence
927:"Merging Information Under Constraints: A Logical Framework"
541:
Management of Heterogeneous and Autonomous Database Systems
188:
is consistent, then f(P,c) equals this logical conjunction.
1109:
Chopra, Samir; Ghose, Aditya; Meyer, Thomas (2006-03-01).
1474:
1367:"Conciliation and Consensus in Iterated Belief Merging"
1148:
Everaere, P.; Konieczny, S.; Marquis, P. (2007-02-06).
956:
Konieczny, SĂ©bastien; Pino PĂ©rez, RamĂłn (2005-02-01).
822:
Konieczny, SĂ©bastien; Pino PĂ©rez, RamĂłn (2011-04-01).
1481:
to it so that it can be listed with similar articles.
1072:
Meyer, Thomas; Ghose, Aditya; Chopra, Samir (2001).
781:
IEEE Transactions on Knowledge and Data Engineering
697:
IEEE Transactions on Knowledge and Data Engineering
365:correspond to agens, then this corresponds to the
1076:. In Benferhat, Salem; Besnard, Philippe (eds.).
964:. Decision Analysis and Artificial Intelligence.
418:Chpora, Ghose and Meyer relate belief-merging to
1117:. Logic-based Approaches to Information Fusion.
1031:Konieczny, S; Lang, J; Marquis, P (2004-08-01).
888:Konieczny, SĂ©bastien; PĂ©rez, RamĂłn Pino (1999).
250:is consistent iff the logical conjunction of f(p
777:"Arbitration (or how to merge knowledge bases)"
691:Baral, C.; Kraus, S.; Minker, J. (1991-06-01).
1333:Multi-Winner Voting with Approval Preferences
1150:"The Strategy-Proofness Landscape of Merging"
892:. In Hunter, Anthony; Parsons, Simon (eds.).
238:models c, then the logical conjunction of f(p
8:
1207:Haret, Adrian; Wallner, Johannes P. (2019).
372:Minimizing the largest distance between the
346:Minimizing the sum of distances between the
1154:Journal of Artificial Intelligence Research
520:- aggregating data from different sensors.
1306:
1175:
1165:
1048:
997:"Belief Merging and Judgment Aggregation"
635:
330:is consistent, then f(P, conjunction of c
1330:Lackner, Martin; Skowron, Piotr (2023).
962:European Journal of Operational Research
434:hold in their belief-merging framework.
1074:"Social Choice, Merging, and Elections"
530:
147:different experts, and another formula
1013:
1002:
407:Belief merging is somewhat related to
361:or another metric). If the formulas p
7:
1260:. ECAI'16. NLD: IOS Press: 372–380.
890:"Merging with Integrity Constraints"
775:Liberatore, P.; Schaerf, M. (1998).
693:"Combining Multiple Knowledge Bases"
624:ACM Transactions on Database Systems
613:
611:
563:
561:
143:), representing e.g. claims made by
869:Konieczny, SĂ©bastien (2000-04-11).
1466:needs additional or more specific
618:Subrahmanian, V. S. (1994-06-01).
586:10.1111/j.1467-8640.1992.tb00337.x
14:
1407:Pigozzi, Gabriella (2006-09-01).
1213:Logics in Artificial Intelligence
995:Pigozzi, Gabriella (2015-07-08).
1455:
931:Journal of Logic and Computation
403:Belief merging and social choice
322:IC8: If the conjunction of f(P,c
121:that takes as input a vector of
730:Revesz, Peter Z. (1993-08-01).
462:A new suggested rule, based on
828:Journal of Philosophical Logic
620:"Amalgamating knowledge bases"
284:IC6: If the conjunction of f(P
43:. It also has applications in
1:
1291:"Proportional Belief Merging"
1266:10.3233/978-1-61499-672-9-372
428:Gibbard–Satterthwaite theorem
424:Arrow's impossibility theorem
303:IC7: The conjunction of f(P,c
1127:10.1016/j.inffus.2005.05.003
1050:10.1016/j.artint.2004.04.008
925:Konieczny, S. (2002-10-01).
464:Proportional approval voting
415:and preference aggregation.
311:models f(P, conjunction of c
166:, then f(P,c) is consistent.
25:propositional belief merging
1221:10.1007/978-3-030-19570-0_9
292:,c) is consistent, then f(P
265:IC5: The conjunction of f(P
1524:
1039:. Nonmonotonic Reasoning.
974:10.1016/j.ejor.2003.06.039
574:Computational Intelligence
1425:10.1007/s11229-006-9063-7
840:10.1007/s10992-011-9175-5
668:"Modern database systems"
125:consistent (satisfiable)
35:) and combining multiple
1369:. In Godo, LluĂs (ed.).
1308:10.1609/aaai.v34i03.5671
1086:10.1007/3-540-44652-4_41
902:10.1007/3-540-48747-6_22
449:justified representation
1037:Artificial Intelligence
1033:"DA2 merging operators"
943:10.1093/logcom/12.5.773
1012:Cite journal requires
219:) is equivalent to f(P
127:propositional formulas
824:"Logic Based Merging"
744:10.1145/153850.153857
637:10.1145/176567.176571
493:Judgement aggregation
422:. They show that the
477:Other related fields
397:polynomial hierarchy
70:first-order theories
1384:10.1007/11518655_44
1336:. Springer Nature.
544:. Morgan Kaufmann.
483:social epistemology
171:logical conjunction
45:multi-agent systems
1342:20.500.12657/60149
1115:Information Fusion
512:Belief aggregation
471:Multiwinner voting
207:is equivalent to c
1496:
1495:
1479:adding categories
1393:978-3-540-31888-0
1351:978-3-031-09016-5
1275:978-1-61499-671-2
1230:978-3-030-19570-0
1177:10.1613/jair.2034
1095:978-3-540-44652-1
911:978-3-540-48747-0
793:10.1109/69.667090
753:978-0-89791-593-9
551:978-1-55860-216-8
420:strategyproofness
387:, refined by the
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359:Hamming distance
115:merging operator
74:annotated logics
29:logical formulae
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968:(3): 785–802.
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19:, also called
17:Belief merging
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1487:November 2023
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1121:(1): 61–79.
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787:(1): 76–90.
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675:. Retrieved
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