Abstract
This paper shows the equivalence of three ways of expressing a certain strong consistency constraint — called the fulfilment constraint — on proofs of the logic of reusable propositional output: as a global requirement on proofs, as a local requirement on labels of formulas, and by phasing of proof rules. More specifically, we first show that the fulfilment constraint may be expressed either as a requirement on the historical structure of the proof tree or as a requirement on the contents of labels attached to its nodes. Second, we show that labelled proofs may be rewritten into a tightly phased form in which rules are applied in a fixed order. Third, we show that when a proof is in such a phased form, the consistency check on labels becomes redundant.
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van der Torre, L. (2000). The Logic of Reusable Propositional Output with the Fulfilment Constraint. In: Basin, D., D’Agostino, M., Gabbay, D.M., Matthews, S., Viganò, L. (eds) Labelled Deduction. Applied Logic Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4040-9_10
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DOI: https://doi.org/10.1007/978-94-011-4040-9_10
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