Knot is not that nasty

Synthese 198 (S22):5533-5554 (2019)
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Abstract

In this paper, we evaluate Button’s claim that knot is a nasty connective. Knot’s nastiness is due to the fact that, when one extends the set \ with knot, the connective provides counterexamples to a number of classically valid operational rules in a sequent calculus proof system. We show that just as going non-transitive diminishes tonk’s nastiness, knot’s nastiness can also be reduced by dropping Reflexivity, a different structural rule. Since doing so restores all other rules in the system as validity-preserving, we are inclined to conclude that there, knot is not that nasty. However, since motivating non-reflexivity is harder than motivating non-transitivity, we also acknowledge that disagreement with our conclusion is possible.

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Luis Estrada-González
National Autonomous University of Mexico

Citations of this work

Knot much like tonk.Michael De & Hitoshi Omori - 2022 - Synthese 200 (149):1-14.

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References found in this work

The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.
Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.

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