A Syntactical Approach to Qualitative Constraint Networks Merging

Abstract

We address the problem of merging qualitative constraint networks (QCNs) representing agents local preferences or beliefs on the relative position of spatial or temporal entities. Two classes of merging operators which, given a set of input QCNs defined on the same qualitative formalism, return a set of qualitative configurations representing a global view of these QCNs, are pointed out. These operators are based on local distances and aggregation functions. In contrast to QCN merging operators recently proposed in the literature, they take account for each constraint from the input QCNs within the merging process. Doing so, inconsistent QCNs do not need to be discarded at start, hence agents reporting locally consistent, yet globally inconsistent pieces of information (due to limited rationality) can be taken into consideration.

Applying Belief Revision to Case-Based Reasoning

“…A qualitative constraint network (QCN) is a knowledge base of a QA; it is given by a set of constraints between variables. Belief revision has been studied for QAs in [26]: a revision operator associating to a QCN ψ and a QCN μ a QCN ψ μ is defined, following principles of distance-based revision operators. 7 Therefore, revision-based adaptation can be applied to a CBR system in which cases are represented by QCNs.…”

Belief revision in the propositional closure of a qualitative algebra (extended version)

“…For instance, belief merging has been studied for qualitative algebras by Condotta et al (2010) and Wallgrün and Dylla (2010). Wallgrün and Dylla have proposed syntax-based revision operators for qualitative algebras.…”

“…In particular, it is rather simple to define a revision operator on a qualitative algebra (such as the Allen algebra) by reusing the work of Condotta et al (2010) about the related issue of belief merging. The result of such a belief revision is a set of belief bases to be interpreted disjunctively, and which is not necessarily representable as a sole belief base: qualitative algebras are not closed under disjunction.…”

Revising Qualitative Constraint Networks: Definition and Implementation

“…We briefly recall concepts of merging information in the context of QCNs as detailed in recent works [WD10], [CKMS10]. Some of these works even propose a framework for merging heterogeneous QCNs [CKMS09a], but in this paper we will only consider revising beliefs according to QCNs expressed over the same calculus.…”

“…Such issues arise in, e.g., the context of robots learning a map of their surroundings [Wal10]. Several operators have been studied for merging QCNs (see [WD10], [CKMS09a], [CKMS10], [CKMS09b]). These merging operators are based on the distance between solutions of each source (called semantic operators) or based on the number of violated constraints (called syntactic operators).…”