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Normalisation for Classical Bilateral Logic with some Philosophical Remarks

Kurbis, N; (2021) Normalisation for Classical Bilateral Logic with some Philosophical Remarks. Journal of Applied Logic , 8 (2) pp. 531-556. Green open access

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Abstract

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 compara- ble to Prior’s tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and elimi- nating 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 clos- ing 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.

Type: Article
Title: Normalisation for Classical Bilateral Logic with some Philosophical Remarks
Open access status: An open access version is available from UCL Discovery
Publisher version: https://collegepublications.co.uk/ifcolog/?00044
Language: English
Additional information: This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10122319
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