Abstract
In several different settings, one comes across situations in which the objects of study are locally consistent but globally inconsistent. Earlier work on probability distributions in the 1960s and relational database theory in the 1980s produced characterizations of when local consistency implies global consistency. We will discuss a common generalization of these results by considering K-relations over an arbitrary positive semiring K and establishing that a collection H of sets of attributes has the property that every pairwise consistent collection of K-relations over those sets of attributes is globally consistent if and only if the collection H forms an acyclic hypergraph.
This is joint work with Albert Atserias at UPC Barcelona. It appeared as a chapter with the same title in the recently published volume “Samson Abramsky on Logic and Structure in Computer Science and Beyond” in the Outstanding Contributions to Logic book series
https://link.springer.com/book/10.1007/978-3-031-24117-8
See also https://arxiv.org/abs/2009.09488