Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose a new bi-intuitionistic type theory called Dualized Type Theory#N#(DTT). It is a simple type theory with perfect intuitionistic duality, and#N#corresponds to a single-sided polarized sequent calculus.  prove DTT strongly#N#normalizing, and prove type preservation. DTT is based on a new propositional#N#bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds#N#on Pinto and Uustalu's logic L. DIL is a simplification of L by removing#N#several admissible inference rules while maintaining consistency and#N#completeness. Furthermore, DIL is defined using a dualized syntax by labeling#N#formulas and logical connectives with polarities thus reducing the number of#N#inference rules needed to define the logic.  give a direct proof of#N#consistency, but prove completeness by reduction to L.
['Harley D. Eades', 'Aaron Stump', 'Ryan McCleeary']
I am writing a research paper on a idea Dualized Simple Type Theory
[{"from": "human", "value": "I am writing a research paper on a idea Dualized Simple Type Theory"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose a new bi-intuitionistic type theory called Dualized Type Theory#N#(DTT). It is a simple type theory with perfect intuitionistic duality, and#N#corresponds to a single-sided polarized sequent calculus.  prove DTT strongly#N#normalizing, and prove type preservation. DTT is based on a new propositional#N#bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds#N#on Pinto and Uustalu's logic L. DIL is a simplification of L by removing#N#several admissible inference rules while maintaining consistency and#N#completeness. Furthermore, DIL is defined using a dualized syntax by labeling#N#formulas and logical connectives with polarities thus reducing the number of#N#inference rules needed to define the logic.  give a direct proof of#N#consistency, but prove completeness by reduction to L."}]