Structuring Co-constructive Logic for Proofs and Refutations

Logica Universalis 10 (1):67-97 (2016)

Authors
James Trafford
University For The Creative Arts
Abstract
This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following Trafford :22–40, 2015). It is notoriously tricky to define a proof-theoretic semantics for logics that adequately represent constructivity over proofs and refutations. By developing abstractions of elementary topoi, we consider an elementary topos as structure for proofs, and complement topos as structure for refutation. In doing so, it is possible to consider a dialogue structure between these topoi, and also control their relation such that classical logic is simulated where proofs and refutations are conclusive.
Keywords Constructive logic  category theory  topos  intuitionistic  co-intuitionistic
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DOI 10.1007/s11787-016-0138-z
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References found in this work BETA

Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
Structure in Mathematics and Logic: A Categorical Perspective.S. Awodey - 1996 - Philosophia Mathematica 4 (3):209-237.
Why Conclusions Should Remain Single.Florian Steinberger - 2011 - Journal of Philosophical Logic 40 (3):333-355.
Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.

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