  We establish a strong link between two apparently unrelated topics: the study
of conflicting information in the formal framework of valuation algebras, and
the phenomena of non-locality and contextuality. In particular, we show that
these peculiar features of quantum theory are mathematically equivalent to a
general notion of \emph{disagreement} between information sources. This result
vastly generalises previously observed connections between contextuality,
relational databases, constraint satisfaction problems, and logical paradoxes,
and gives further proof that contextual behaviour is not a phenomenon limited
to quantum physics, but pervades various domains of mathematics and computer
science. The connection allows to translate theorems, methods and algorithms
from one field to the other, and paves the way for the application of generic
inference algorithms to study contextuality.
