If the axioms are demonstrable only relative to an arbitrarily chosen construction, they are not demonstrated in an absolute logical sense but merely shown to be consistent within one model.
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Propositions that we assume to be true and necessary, originating in the content of judgments.
consistent(Contrasted with the model-theoretic notion of satisfiability)
A proof-theoretic notion indicating that no contradiction is derivable from a set of sentences
model(Possible worlds interpretation of S5 adapted for modal nonmonotonic logic)
A pair <I, S> where I is a set of literals (a state description / possible world) and S is a set of complete, consistent sets of literals (interpretations) with I ∈ S