When Structural Principles Hold Merely Locally

In Pavel Arazim & Tomáš Lávička (eds.), The Logica Yearbook 2016. London: College Publications. pp. 53-67 (2017)
Authors
Ulf Hlobil
Concordia University
Abstract
In substructural logics, structural principles may hold in some fragments of a consequence relation without holding globally. I look at this phenomenon in my preferred substructural logic, in which Weakening and Cut fail but which is supra-intuitionistic. I introduce object language operators that keep track of the admissibility of Weakening and of intuitionistic implications. I end with some ideas about local transitivity.
Keywords nontransitive logic  substructural logic  nonmonotonic logic  structural principles  inferentialism  logical expressivism  atomic systems
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