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

lmcs:2005 - Logical Methods in Computer Science, August 15, 2016, Volume 12, Issue 3
Dualized Simple Type Theory

Authors: Eades III, Harley and Stump, Aaron and McCleeary, Ryan

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.


Source : oai:arXiv.org:1605.01083
DOI : 10.2168/LMCS-12(3:2)2016
Volume: Volume 12, Issue 3
Published on: August 15, 2016
Submitted on: August 15, 2016
Keywords: Computer Science - Logic in Computer Science,F.3.2


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