Abstract
In this tutorial we will present the foundations of the belief merging operators:
a model of fusion information based on logical representation of the information.
We will give constructive methods for building operators aiming to merge pieces
of information coming from several sources.
Description
Belief merging aims at combining several pieces of information when there is no strict precedence between them.
The agent faces several conflicting pieces of information coming from several sources of equal reliability and he has to build
a coherent description of the world from them.
The aim of this Tutorial is to give an account of the main tools developed in last years in the area of belief merging. We will focus on the case where
the pieces of information have logical representations.
Rationality postulates, like in belief revision, have been proposed to characterize belief merging operators.
These postulates are closely related to the revision ones. Nevertheless there is an important difference, namely the social aspect of merging: one needs some postulates to say how to solve the conflicts between the sources of information.
So it is possible to distinguish different families of merging operators, depending on their behavior with respect to the sources, like a majority behavior for instance.
An important aspect of this logical characterization is the possibility of stating representation theorems that provide a constructive way to define merging operators satisfying all the desired logical properties. We will develop these constructive methods.
Justification
Belief merging is an important issue of many AI fields. In particular, the problem of merging multiple sources of information is especially important in distributed databases, multi-agent systems, and in distributed information systems.
Inconsistency problems can occur when one wants to combine several sources of information. Consider a set of belief bases coding the belief of
several human experts. In order to build a general expert system it is reasonable to try to combine all these belief bases in a single belief base that expresses the belief of the expert group. This process allows to discover new pieces of belief distributed among the sources.
For example if an expert knows that A is true and another knows that A→B holds, then the synthesized belief knows that B is true whereas none of the experts knows it.
This was called implicit belief by Halpern and Moses [15]
However, to simply put these belief bases together is a wrong solution since there could certainly be contradictions between some experts. Thus, having techniques to perform this task in a coherent and predictive way is important in areas of AI concerning distributed information.
Potential target
Novices aiming to discover a new topic in AI. Expert non specialists aiming to become acquainted with
logical approaches to merging information.
Prerequisite
A basic course in Mathematical Logic.
Objectives
References
[1] Konieczny, S. and R. Pino P.érez: 1998, `On the logic of Merging'. In Proceedings of the Sixth International Conference on Principles of Knowledge Representation And Reasoning, KR'98. Trento, Italy. June 2-5, 1998, pp 488-498. Morgan-Kaufmann Publishers.
[2] Konieczny, S. and R. Pino P.érez: 2002a, `Merging information under constraints: a logical framework'. Journal of Logic and Computation 12(5), 773-808.
[3] Konieczny, S. and R. Pino P.érez: 2011, `Logic Based Merging'. Journal of Philosophical Logic, 40: 239-270.
[4] Konieczny, S. and R. Pino P.érez: 1999, `Merging with integrity constraints'. In Proceedings of the Fifth European Conference on Symbolic and Quantitatives Approaches to Reasoning with Uncertainty, ECSQARU'99, London, UK, July 1999, Lecture Notes in Arti.cial Intelligence, vol. 1638, pp 233{244, Springer, 1999.
[5] Konieczny, S. and R. Pino P.érez: 2002b, `On the frontier between arbitration and majority'. In: Eighth International Conference on Principles of Knowledge Representation and Reasoning (KR'02). pp. 109-118.
[6] Konieczny, S. and R. Pino P.érez: 2005, Propositional belief base merging or how to merge beliefs/goals coming from several sources and some links with social choice theory'. European J. Oper. Res. 160 (3) 785-802.
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[15] Halpern, J. and Y. Moses: 1992, `A guide to completeness and complexity for modal logics of knowledge and belief'. Arti.cial Intelligence 54 (3), 319-379.