  Inspired by classic work of Wallman and more recent work of
Jung-Kegelmann-Moshier and Vickers, we show how to encode general subbases of
stably locally compact spaces via certain entailment relations. We further
build this up to a categorical duality encompassing the classic Priestley-Stone
duality and its various extensions to stably locally compact spaces by Shirota,
De Vries, Hofmann-Lawson (in the stable case), Jung-S\"underhauf,
Hansoul-Poussart, Bezhanishvili-Jansana, van Gool and Bice-Starling.
