Majority Merging: From Boolean Spaces to Affine Spaces
Abstract
This paper is centered on the problem of merging (possibly conflicting) information coming from different sources. Though this problem has attracted much attention in propositional settings, propositional languages remain typically not expressive enough for a number of applications, especially when spatial information must be dealt with. In order to fill the gap, we consider a (limited) first-order logical setting, expressive enough for representing and reasoning about information modeled as half-spaces from metric affine spaces. In this setting, we define a family of distance-based majority merging operators which includes the propositional majority operator $Delta^{d_H, sum}$. We identify a subclass of interpretations of our representation language for which the result of the merging process can be computed and expressed as a formula.