Model-based belief merging without distance measures

Abstract

Merging operators try to define the beliefs of a group of agents according to the beliefs of each member of the group. Several model-based propositional belief merging operators have been proposed which use distance measures and aggregation functions. This paper introduces the notion of Partial Satisfiability which is an alternative way of measuring the satisfaction of a formula since this notion lets us have satisfaction values in the interval [0,1]. Partial Satisfiability allows us to define model-based merging operator. The proposal produces similar results to other merging approaches, but while other approaches require many merging operators in order to achieve satisfactory results for different scenarios this proposal obtains similar results for all these different scenarios with a unique operator. Moreover, unlike most of model-based approaches, this approach considers the case where the belief bases are inconsistent. The framework presented is in a preliminary state and further analysis of its properties is needed in order to characterize the proposed merging operator in terms of postulates. 625 978-81-904262-7-5 (RPS) c 2007 IFAAMAS

Implementing Δ_ps (PS-Merge) Belief Merging Operator for Belief Revision

“…In [5] the notion of Partial Satisfiability (PS) is introduced which is a generalization of satisfiability, in which the valuation function w :…”

“…An alternative distance between possible worlds has been defined in [5]. This distance is based on the notion of Partial Satisfiability (PS).…”

“…This distance is based on the notion of Partial Satisfiability (PS). A merging operator based on PS-distance is also proposed in [5]. The PS-operator has been implemented avoiding the computation of the models of the belief profile.…”

“…In the literature, we found that belief merging can be extended to support integrity constraints, which are typically represented as a set of formulae or a single formula that must be respected by the merging result 1 . In [5], however, the support of integrity constraints is not considered by the proposed operator. Note that as showed in [22], a model-based merging operator can be naturally extended to support integrity constraints.…”

Nutritional Menu Planning: A Hybrid Approach and Preliminary Tests

“…Operator. This belief merging operator is an alternative way to distance-based operators [11,16,18,25] or to syntax-based operators [2,19], as it is based on the notion of Partial Satisfiability [5]. PS-Merge produces similar results to other merging approaches, but while other approaches require many merging operators in order to achieve satisfactory results for different scenarios, this approach obtains similar results for all these different scenarios with a unique operator [24].…”