Galois Theory for Partial Clones and Some Relational Clones

A Galois connection between partial clones and a new variant of relation algebras is established. We introduce a new elementary operation on relations which captures the difference between total and partial clones and allows us to adapt the proof of the Galois connection from the total case to the partial case. This Galois connection is able to capture all partial clones and is not restricted to strong partial clones as in previous work.