# K-consistency

### From Glossary

A consistency notion in constraint programming.

Let be a CSP.

- Given a set of variables with , a locally consistent instantiation on is
*k-consistent*iff for any*k*th variable there exists a value such that is locally consistent. - The CSP is
*k-consistent*iff for any set of variables, any locally consistent instantiation on is k-consistent.

For example, 3-consistency ensures that any instantiation any pair of variables can be extended to an instantiation involving any third variable without violating any constraint. It is equivalent to path consistency. Similarly, 2-consistency is also known as arc consistency.