Structural entailment

We give a number of characterizations of structural entailment. In particular, we show that an alter ego structurally entails an algebraic relation s on a finite algebra if and only if s can be obtained via a local construct from . We show, via a range of applications, that, whereas entailment is important in the study of dualisability, structural entailment is important in the study of full and strong dualisability. We also give an application to the transfer of strong dualities that connects this paper to our earlier paper [9] on full versus strong duality.