Hitoshi Omori
Reports on Mathematical Logic, Number 51, 2016, pp. 133-144
https://doi.org/10.4467/20842589RM.16.009.5286The present note corrects an error made by the author in answering an open problem of axiomatizing an expansion of Nelson's logic introduced by Heinrich Wansing. It also gives a correct axiomatization that answers the problem by importing some results on subintuitionistic logics presented by Greg Restall.
Hitoshi Omori
Reports on Mathematical Logic, Number 56, 2021, pp. 75-99
https://doi.org/10.4467/20842589RM.21.004.14376We investigate an expansion of positive intuitionistic logic obtained by adding a constant Ω introduced by Lloyd Humberstone. Our main results include a sound and strongly complete axiomatization, some comparisons to other expansions of intuitionistic logic obtained by adding actuality and empirical negation, and an algebraic semantics. We also brie y discuss its connection to classical logic.
Hitoshi Omori
Reports on Mathematical Logic, Number 50, 2015, pp. 41-51
https://doi.org/10.4467/20842589RM.15.003.3912The present note o ers an axiomatization for an expansion of Nelson's logic motivated by Heinrich Wansing which serves as a base logic for the framework of nonmonotonic reasoning considered by Dov Gabbay and Raymond Turner. We also show that the expansion of Wansing is not conservative intuitionistic logic, but at least as strong as Jankov's logic.