Trafford, James (2015) Duality and inferential semantics. Axiomathes. ISSN 1122-1151 (Print) 1572-8390 (Online)
Creators: | Trafford, James |
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Description/Abstract: | It is well known that classical inferentialist semantics runs into problems regarding abnormal valuations [3, 6, 10]. 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 Greg Restall [13], with the guiding interpretation that the valid sequent Γ \vdash ∆ says that the simultaneous assertion of all of Γ with the denial of all of ∆ is incoherent. However, such structures face significant interpretive challenges [14, 19, 20], and they do not provide an adequate grasp on the machinery of the duality of assertions and denials that could (a) provide an abstract account of inferential semantics; (b) 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. |
Item Type: | Article |
Official URL: | http://link.springer.com/journal/10516 |
Date: | 9 January 2015 |
Identification Number: | 10.1007/s10516-014-9263-6 |
Additional Information: | The final publication is available at Springer via http://dx.doi.org/10.1007/s10516-014-9263-6 |
Schools: | School of Communication Design |
Depositing User: |
Dr James Trafford
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Date Deposited: | 21 Dec 2014 12:39 |
Last Modified: | 08 Jan 2018 14:17 |
URI: | https://research.uca.ac.uk/id/eprint/2012 |
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