Bilateral Inversion Principles

Electronic Proceedings in Theoretical Computer Science 358:202–215 (2022)
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This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguish it from Francez's.



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Nils Kürbis
Ruhr-Universität Bochum

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References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge, Mass.: Harvard University Press.
Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
The runabout inference ticket.Arthur Prior - 1967 - In Peter Strawson (ed.), Analysis. Oxford University Press. pp. 38-9.

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