Journal of Applied Logics 2 (8):531-556 (2021)

Nils Kürbis
University of Lodz
Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem is to count formulas as maximal that are the conclusion of reductio and major premise of an elimination rule and to require their removability from deductions. The main part of the paper consists in a proof of a normalisation theorem for bilateral logic. The closing sections address philosophical concerns whether the proof provides a satisfactory solution to the problem at hand and confronts bilateralists with the dilemma that a bilateral notion of stability sits uneasily with the core bilateral thesis.
Keywords Assertion  Denial  Negation  Speech acts  Normalisation  Logic  Proof Theory
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References found in this work BETA

The Runabout Inference Ticket.Arthur Prior - 1967 - In Peter Strawson (ed.), Analysis. Oxford University Press. pp. 38-9.
[Omnibus Review].Dag Prawitz - 1991 - Journal of Symbolic Logic 56 (3):1094-1096.
The Revival of Rejective Negation.Lloyd Humberstone - 2000 - Journal of Philosophical Logic 29 (4):331-381.
On Inversion Principles.Enrico Moriconi & Laura Tesconi - 2008 - History and Philosophy of Logic 29 (2):103-113.
A More General General Proof Theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.

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