caa a22 4500 605475318 CHVBK 20210128100351.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10516-014-9263-6 doi (NATIONALLICENCE)springer-10.1007/s10516-014-9263-6 Trafford James UCA, Epsom Campus, Epsom, KT18 5BE, Surrey, UK aut Duality and Inferential Semantics [Elektronische Daten] [James Trafford] It is well known that classical inferentialist semantics runs into problems regarding abnormal valuations (Carnap in Formalization of logic. Harvard University Press, Cambridge, 1943; Hjortland in Notre Dame J Formal Logic 55(4):445-467, 2014; Peregrin in J Philos Logic 39(3):255-274, 2010). 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 (Logic, methodology and philosophy of science: proceedings of the twelfth international congress. Kings College Publications, pp 189-205, 2005), 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 (Rumfitt in Grazer Philos Stud 77(1):61-84, 2008; Steinberger in J Philos Logic 40(3):333-355, 2011; Tennant in The taming of the true. Oxford University Press, Oxford, 1997), 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. Springer Science+Business Media Dordrecht, 2015 Inferentialism nationallicence Proof nationallicence Refutation nationallicence Multiple-conclusion nationallicence Semantics nationallicence Sequent nationallicence Axiomathes Springer Netherlands 25/4(2015-12-01), 495-513 1122-1151 25:4<495 2015 25 10516 https://doi.org/10.1007/s10516-014-9263-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10516-014-9263-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Trafford James UCA, Epsom Campus, Epsom, KT18 5BE, Surrey, UK aut NATIONALLICENCE 773 0- Axiomathes Springer Netherlands 25/4(2015-12-01), 495-513 1122-1151 25:4<495 2015 25 10516