Duality and Inferential Semantics

Axiomathes 25 (4):495-513 (2015)
Authors
James Trafford
University For The Creative Arts
Abstract
It is well known that classical inferentialist semantics runs into problems regarding abnormal valuations. It is equally well known that the issues can be resolved if we construct the inference relation in a multiple-conclusion sequent calculus. The latter has been prominently developed in recent work by Restall, with the guiding interpretation that the valid sequent says that the simultaneous assertion of all of Γ with the denial of all of Δ is incoherent. However, such structures face significant interpretive challenges, and they do not provide an adequate grasp on the machinery of the duality of assertions and denials that could provide an abstract account of inferential semantics; show why the dual treatment is semantically superior. This paper explores a slightly different tack by considering a dual-calculus framework consisting of two, single-conclusion, inference relations dealing with the preservation of assertion and the preservation of denial, respectively. In this context, I develop an abstract inferentialist semantics, before going on to show that the framework is equivalent to Restall’s, whilst providing a better grasp on the underlying proof-structure
Keywords Inferentialism  Proof  Refutation  Multiple-conclusion  Semantics  Sequent
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DOI 10.1007/s10516-014-9263-6
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References found in this work BETA

The Taming of the True.Neil Tennant - 1997 - Oxford University Press.
Multiple Conclusions.Greg Restall - 2005 - In Petr Hájek, Luis Valdés-Villanueva & Dag Westerståhl (eds.), Logic, Methodology and Philosophy of Science. College Publications.

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