  A natural and established way to restrict the constraint satisfaction problem
is to fix the relations that can be used to pose constraints; such a family of
relations is called a constraint language. In this article, we study arc
consistency, a heavily investigated inference method, and three extensions
thereof from the perspective of constraint languages. We conduct a comparison
of the studied methods on the basis of which constraint languages they solve,
and we present new polynomial-time tractability results for singleton arc
consistency, the most powerful method studied.

Artificial Intelligence;Computational Complexity;Logic in Computer Science