Structuring co-constructive logic for proofs and refutations

Trafford, James (2016) Structuring co-constructive logic for proofs and refutations. Logica Universalis, 10 (1). pp. 67-97. ISSN 1661-8297

Creators:
Trafford, James
Description/Abstract:

This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following. 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 (interpreted in a Boolean topos) is simulated where proofs and refutations are conclusive.

Item Type:
Article
Official URL:
http://www.springer.com/birkhauser/mathematics/jou...
Date:
5 February 2016
Identification Number:
10.1007/s11787-016-0138-z
Additional Information:

The final publication is available at Springer via http://dx.doi.org/10.1007/s11787-016-0138-z

Uncontrolled Keywords or tags :
constructive logic, category theory, topos, intuitionistic, co-intuitionistic
Schools:
School of Communications
Depositing User:
Dr James Trafford
Date Deposited:
27 Jan 2016 16:41
Last Modified:
05 Mar 2022 04:31
Trafford, James:
ORCID iD: https://orcid.org/0000-0002-6762-2918
URI:
https://research.uca.ac.uk/id/eprint/2985

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