Displaying and deciding substructural logics 1: Logics with contraposition

Journal of Philosophical Logic 27 (2):179-216 (1998)
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Abstract

Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic. However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory to show decidability for a large range of substructural logics.

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Greg Restall
University of Melbourne

References found in this work

Entailment: The Logic of Relevance and Neccessity, Vol. I.Alan Ross Anderson & Nuel D. Belnap - 1975 - Princeton, N.J.: Princeton University Press. Edited by Nuel D. Belnap & J. Michael Dunn.
Linear Logic.Jean-Yves Girard - 1987 - Theoretical Computer Science 50:1–101.
Display logic.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (4):375-417.
The undecidability of entailment and relevant implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.

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