On the semantics of theory change

TLDR

Theory change has traditionally been split into revision and update, but this work argues for a third type—arbitration—where new information is treated as an additional, equally weighted voice, implying commutativity. The authors introduce arbitration as a third category of theory change. Arbitration is defined by a set of postulates and a model‑theoretic characterization for propositional theories, with an extension to weighted arbitration assigning different weights to models.

Abstract

Katsuno and Mendelzon divide theory change, the problem of adding new information to a logical theory, into two types: revision and update. We propose a third type of theory change: arbitration. The key idea is the following: the new information is considered neither better nor worse than the old information represented by the logical theory. The new information is simply one voice against a set of others already incorporated into the logical theory. From this follows that arbitration should be commutative. First we define arbitration by a set of postulates and then describe a model-theoretic characterization of arbitration for the case of propositional logical theories. We also study weighted arbitration where different models of a theory can have different weights.