Duality and Inferential Semantics

Axiomathes 25 (4):495-513 (2015)
James Trafford
University For The Creative Arts
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
Categories (categorize this paper)
DOI 10.1007/s10516-014-9263-6
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 33,190
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

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.

View all 21 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles


Added to PP index

Total downloads
11 ( #463,433 of 2,242,290 )

Recent downloads (6 months)
1 ( #410,280 of 2,242,290 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature