Structuring Co-constructive Logic for Proofs and Refutations

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

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,168

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
Linearizing intuitionistic implication.Patrick Lincoln, Andre Scedrov & Natarajan Shankar - 1993 - Annals of Pure and Applied Logic 60 (2):151-177.
A Type Theory With Mixed Constructivity And Assignments.James Sasaki - 1997 - Logic Journal of the IGPL 5 (3):67-104.
Axioms for classical, intuitionistic, and paraconsistent hybrid logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
Constructive sheaf semantics.Erik Palmgren - 1997 - Mathematical Logic Quarterly 43 (3):321-327.
Strongly uniform bounds from semi-constructive proofs.Philipp Gerhardy & Ulrich Kohlenbach - 2006 - Annals of Pure and Applied Logic 141 (1):89-107.

Analytics

Added to PP
2016-02-06

Downloads
18 (#614,279)

6 months
1 (#448,551)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

James Trafford
University For The Creative Arts

Citations of this work

Add more citations

References found in this work

Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
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.

View all 34 references / Add more references