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Forthcoming papers


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Normalisation for Bilateral Classical Logic with some Philosophical Remarks

Assertion and Proof special issue

Nils Kürbis

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 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 require their removability from deductions. Other formulas should count as maximal within bilateral logic, too. 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 confront bilateralists with the dilemma that abilateral notion of stability sits uneasily with the core bilateral thesis






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