A general framework for representing belief change is presented, based on notions of minimal change. A problem instance in the approach is made up of an undirected graph in which a formula is associated with each vertex of the graph. Edges give connectivity between vertices, and can be used to define a notion of distance between vertices. For example, vertices may represent spatial locations, points in time, or some other notion of locality in some (concrete or abstract) space; edges may represent spatial proximity, temporal adjacency, some other notion of adjacency, respectively. Information is shared between vertices via a process of minimisation over the graph.
Semantic and syntactic characterisations of this minimisation are given, and shown to be equivalent. While providing a general model of information sharing in arbitrary settings modelable by a graph, we also show that this approach is general enough to capture existing minimisation-based approaches to belief merging, belief revision, and (temporal) extrapolation operators.
While we focus on a set-theoretic notion of minimisation, we also consider other approaches, such as cardinality-based minimisation. A straightforward extension allows weights to be attached to edges, representing notions such as strength of connectivity or priority.