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A Hypersequent Calculus for Classical Contingencies
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DOI：10.1007/s10992-026-09832-y.png)
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Abstract
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We present a hypersequent calculus that is sound and complete with respect to the truth-functionally contingent formulas of classical logic. We investigate its structural properties and provide a Gentzen-style cut-elimination procedure. The most notable feature of the calculus is that it jointly satisfies the subformula property and the property of deductive purity, to the effect that only contingent hypersequents occur in formal proofs. Moreover, since the negation of a contingent formula is also contingent, the calculus turns out to be paraconsistent, and since the conjunction of a formula with its own negation is not contingent, the paraconsistency is of the non-adjunctive kind.
Keywords:
Classical logic
Antisequent
Hypersequent
Contingency
Paraconsistency
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