  Literature on Constraint Satisfaction exhibits the definition of several
structural properties that can be possessed by CSPs, like (in)consistency,
substitutability or interchangeability. Current tools for constraint solving
typically detect such properties efficiently by means of incomplete yet
effective algorithms, and use them to reduce the search space and boost search.
  In this paper, we provide a unifying framework encompassing most of the
properties known so far, both in CSP and other fields literature, and shed
light on the semantical relationships among them. This gives a unified and
comprehensive view of the topic, allows new, unknown, properties to emerge, and
clarifies the computational complexity of the various detection problems.
  In particular, among the others, two new concepts, fixability and
removability emerge, that come out to be the ideal characterisations of values
that may be safely assigned or removed from a variables domain, while
preserving problem satisfiability. These two notions subsume a large number of
known properties, including inconsistency, substitutability and others.
  Because of the computational intractability of all the property-detection
problems, by following the CSP approach we then determine a number of
relaxations which provide sufficient conditions for their tractability. In
particular, we exploit forms of language restrictions and local reasoning.
