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feat(Logic): semantic consequence, with Kleene K3 as an instance - #1156
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This PR adds a logical consequence relation for inference systems whose judgements pair a model with a proposition, and instantiates it for Kleene's strong three-valued logic. The relation has weakening and cut, and contradictory premises entail everything, as usual; these are proved once, generically, over a class of models given as judgemental contexts. However, in K3 the deduction theorem fails: A entails A, but A → A is not valid for
⊥-free A.Kleene consequence is strictly weaker than classical consequence. Restricting to two-valued valuations gives
ClassicalEntails, whichEntailsimplies. Excluded middle separates the two.I used Claude to help write some of the code.