Categorical and Algebraic Aspects of the Intuitionistic Modal Logic IEL^- and its predicate extensions [article]

Daniel Rogozin
2020 arXiv   pre-print
The system of intuitionistic modal logic IEL^- was proposed by S. Artemov and T. Protopopescu as the intuitionistic version of belief logic. We construct the modal lambda calculus which is Curry-Howard isomorphic to IEL^- as the type-theoretical representation of applicative computation widely known in functional programming. We also provide a categorical interpretation of this modal lambda calculus considering coalgebras associated with a monoidal functor on a cartesian closed category.
more » ... , we study Heyting algebras and locales with corresponding operators. Such operators are used in point-free topology as well. We study compelete semantics à la Kripke-Joyal for predicate extensions of IEL^- and related logics using Dedekind-MacNeille completions and modal cover systems introduced by Goldblatt. The paper extends the conference paper published in the LFCS'20 volume.
arXiv:2005.01135v3 fatcat:7f3qvt33dzgmtdl4rcztcv7me4