Australasian Journal of Logic 18 (2):51-72 (2021)

Tore Fjetland Øgaard
University of Bergen
Restall set forth a "consecution" calculus in his "An Introduction to Substructural Logics." This is a natural deduction type sequent calculus where the structural rules play an important role. This paper looks at different ways of extending Restall's calculus. It is shown that Restall's weak soundness and completeness result with regards to a Hilbert calculus can be extended to a strong one so as to encompass what Restall calls proofs from assumptions. It is also shown how to extend the calculus so as to validate the metainferential rule of reasoning by cases, as well as certain theory-dependent rules.
Keywords consecution  external consequence  Hilbert consequence  relevant logic  substructural proof theory
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DOI 10.26686/ajl.v18i2.6770
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References found in this work BETA

The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
Fusion and Confusion.Graham Priest - 2015 - Topoi 34 (1):55-61.

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Confused Entailment.Tore Fjetland Øgaard - 2022 - Topoi 41 (1):207-219.

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