Tree Trimming: Four Non-Branching Rules for Priest’s Introduction to Non-Classical Logic

  • Marilynn Johnson The Graduate Center, City University of New York

Abstract

In An Introduction to Non-Classical Logic: From If to Is Graham Priest (2008) presents branching rules in Free Logic, Variable Domain Modal Logic, and Intuitionist Logic. I propose a simpler, non-branching rule to replace Priest’s rule for universal instantiation in Free Logic, a second, slightly modified version of this rule to replace Priest’s rule for universal instantiation in Variable Domain Modal Logic, and third and fourth rules, further modifying the second rule, to replace Priest’s branching universal and particular instantiation rules in Intuitionist Logic. In each of these logics the proposed rule leads to tableaux with fewer branches. In Intuitionist logic, the proposed rules allow for the resolution of a particular problem Priest grapples with throughout the chapter. In this paper, I demonstrate that the proposed rules can greatly simplify tableaux and argue that they should be used in place of the rules given by Priest.

Author Biography

Marilynn Johnson, The Graduate Center, City University of New York
PhD student in philosophy at the Graduate Center, City University of New York.
Published
2017-12-01
How to Cite
JOHNSON, Marilynn. Tree Trimming: Four Non-Branching Rules for Priest’s Introduction to Non-Classical Logic. The Australasian Journal of Logic, [S.l.], v. 12, n. 2, dec. 2017. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/2066>. Date accessed: 15 nov. 2019. doi: https://doi.org/10.26686/ajl.v12i2.2066.