Arbitration (or how to merge knowledge bases)

Abstract

Knowledge-based systems must be able to "intelligently" manage a large amount of information coming from different sources and at different moments in time. Intelligent systems must be able to cope with a changing world by adopting a "principled" strategy. Many formalisms have been put forward in the artificial intelligence (Al) and database (DB) literature to address this problem. Among them, belief revision is one of the most successful frameworks to deal with dynamically changing worlds. Formal properties of belief revision have been investigated by Alchourron, Gardenfors, and Makinson, who put forward a set of postulates stating the properties that a belief revision operator should satisfy. Among these properties, a basic assumption of revision is that the new piece of information is totally reliable and, therefore, must be in the revised knowledge base. Different principles must be applied when there are two different sources of information and each one has a different view of the situation-the two views contradicting each other. If we do not have any reason to consider any of the sources completely unreliable, the best we can do is to "merge" the two views in a new and consistent one, trying to preserve as much information as possible. We call this merging process arbitration. In this paper, we investigate the properties that any arbitration operator should satisfy. In the style of Alchourron, Gardenfors, and Makinson we propose a set of postulates, analyze their properties, and propose actual operators for arbitration

Quantum-Based Belief Merging

“…The key difference between the proposed operator and the classical definitions of arbitration [12,9,7] is related to the notion of quantum. In the existing definitions of arbitration, the underlying principle is to determine the models that represent a median solution: the solution "is not so far" from each φ i in terms of truth values.…”

“…The initial belief sets may be inconsistent, i.e., φ 1 ∧ · · · ∧ φ n ⊢ ⊥, and thus the aggregation method should merge belief sets φ i in a consistent way. Among the different merging operators, let us mention the well known majority operators [10] and arbitration operators [12,9]. In order to evaluate merging operators general properties have to be asserted.…”

“…The goal of belief merging is to aggregate in a consistent way multiple beliefs usually represented as sets of logical statements so as to obtain a new set of statements [9,7]. This paper considers distance-based belief merging which is based on three main components [6]: a notion of distance between propositional models, a function to aggregate the distances, and a procedure to select the closest eligible resulting sets w.r.t.…”

Merging First-Order Knowledge Using Dilation Operators

“…Merging operators from the literature can be broadly categorised in two groups: the model-based, or semantic, operators are defined using orderings over the models of PL, expressing how close models are with respect to the knowledge bases being merged [2,3,4,5]; and the syntax-based, or consistency-based, operators, where the merging process is defined in terms of consistent unions of subsets of the original knowledge bases [1,10,13]. We believe that the semantic approach offers several advantages such as syntax-independence and generality (e.g.…”

“…In recent years, the area of knowledge merging has seen significant research results, both in proposals for specific merging operators [1,2,3,4,5] as well as in proposals for unifying frameworks, where specific merging operators can be seen as instantiations of these frameworks [6,7,8,9].…”