Classical logic's ex falso is not merely a formal artifact but tracks the metaphysical principle that contradictions are impossible worlds, making any proposition vacuously true there.
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(Relevant to distinguishing contradictions from false contingent statements in the logic student variant of the preface paradox.)
A statement that is necessarily false in all interpretations; in this context, specifically the negation of a tautology or any falsehood drawn from a list containing only tautologies and contradictions.
impossible worlds(Rantala 1982)
A modification to the semantics of epistemic logic in which worlds where logical laws fail are admitted, used to avoid the logical omniscience problem
proposition(Used in the context of a semantic theory sensitive to differences in subject matter.)
The content expressed by a sentence, individuated at least in part by the subject matter of the sentence and the contents of its subsentential expressions.
vacuously true
The status assigned to a universally quantified formula ∀xA in a model with an empty domain, on which it counts as true despite having no instances