In Nicola Olivetti, Rineke Verbrugge & Sara Negri (eds.), Advances in Modal Logic 13. Booklet of Short Papers. Helsinki: pp. 37-43 (2020)

Nils Kürbis
University of Lodz
This paper considers proof-theoretic semantics for necessity within Dummett's and Prawitz's framework. Inspired by a system of Pfenning's and Davies's, the language of intuitionist logic is extended by a higher order operator which captures a notion of validity. A notion of relative necessary is defined in terms of it, which expresses a necessary connection between the assumptions and the conclusion of a deduction.
Keywords Proof-theory  Semantics  Necessity  Validity  Modal Logic  Higher-order rules
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The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
A Mathematical Theory of Evidence.Glenn Shafer - 1976 - Princeton University Press.
Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.
What is a Theory of Meaning? (II).Michael Dummett - 1976 - In Gareth Evans & John McDowell (eds.), Truth and Meaning: Essays in Semantics. Oxford: Clarendon Press.

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