Investigations into a left-structural right-substructural sequent calculus

Journal of Logic, Language and Information 16 (2):141-171 (2007)
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Abstract

We study a multiple-succedent sequent calculus with both of the structural rules Left Weakening and Left Contraction but neither of their counterparts on the right, for possible application to the treatment of multiplicative disjunction against the background of intuitionistic logic. We find that, as Hirokawa dramatically showed in a 1996 paper with respect to the rules for implication, the rules for this connective render derivable some new structural rules, even though, unlike the rules for implication, these rules are what we call ipsilateral: applying such a rule does not make any formula change sides—from the left to the right of the sequent separator or vice versa. Some possibilities for a semantic characterization of the resulting logic are also explored. The paper concludes with three open questions.

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Lloyd Humberstone
Monash University

Citations of this work

Replacement in Logic.Lloyd Humberstone - 2013 - Journal of Philosophical Logic 42 (1):49-89.

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References found in this work

Modal Logic: An Introduction.Brian F. Chellas - 1980 - New York: Cambridge University Press.
Multiple Conclusion Logic.D. J. Shoesmith & Timothy Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press. Edited by T. J. Smiley.
Linear Logic.Jean-Yves Girard - 1987 - Theoretical Computer Science 50:1–102.
Substructural Logics: A Primer.Francesco Paoli - 2002 - Dordrecht, Netherland: Springer.

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