Duality and inferential semantics

Trafford, James (2015) Duality and inferential semantics. Axiomathes. ISSN 1122-1151 (Print) 1572-8390 (Online)

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2012:79217

Duality and inferential semantics (380kB)

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Creators:

Trafford, James

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 Communications