A Nonmonotonic Sequent Calculus for Inferentialist Expressivists

In Pavel Arazim & Michal Dančák (eds.), The Logica Yearbook 2015. College Publications. pp. 87-105 (2016)
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I am presenting a sequent calculus that extends a nonmonotonic consequence relation over an atomic language to a logically complex language. The system is in line with two guiding philosophical ideas: (i) logical inferentialism and (ii) logical expressivism. The extension defined by the sequent rules is conservative. The conditional tracks the consequence relation and negation tracks incoherence. Besides the ordinary propositional connectives, the sequent calculus introduces a new kind of modal operator that marks implications that hold monotonically. Transitivity fails, but for good reasons. Intuitionism and classical logic can easily be recovered from the system.
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