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How should the ontology of a dialetheic world be spelt out?

This is a challenge presented by Graham Priest in his article in the Stanford Encyclopaedia of Philosophy article on dialethiesm.

Dialetheism, in exploding the ubiquitous dichotomy, allows the perception of a world with different levels of certainty, not just at the physical level of, say, quantum mechanics, or at the mathematical level, as shown by Gödel, but at the level of logic. The objection to this is metaphysical - it's an objection to the radical breaching of the confidence in logical certainty by the acceptance that there are true contradictions.

Dialetheism and the perception of reality and consequent removal of "Plato's sunglasses" is a step towards an unblinkered understanding of self and the world. A step on the road to eudæmonia.