Harley Eades III ; Aaron Stump ; Ryan McCleeary - Dualized Simple Type Theory

lmcs:2005 - Logical Methods in Computer Science, April 27, 2017, Volume 12, Issue 3 - https://doi.org/10.2168/LMCS-12(3:2)2016
Dualized Simple Type Theory

Authors: Harley Eades III ; Aaron Stump ; Ryan McCleeary

We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus. We prove DTT strongly normalizing, and prove type preservation. DTT is based on a new propositional bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds on Pinto and Uustalu's logic L. DIL is a simplification of L by removing several admissible inference rules while maintaining consistency and completeness. Furthermore, DIL is defined using a dualized syntax by labeling formulas and logical connectives with polarities thus reducing the number of inference rules needed to define the logic. We give a direct proof of consistency, but prove completeness by reduction to L.

Volume: Volume 12, Issue 3
Published on: April 27, 2017
Accepted on: August 15, 2016
Submitted on: November 19, 2014
Keywords: Computer Science - Logic in Computer Science,F.3.2


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