Abstract:
Connections between certain types of categories (logoses and
toposes) and intuitionistic predicate logic was established in
1960–1970 by Lowvere. The possibility of extending this
connection to some types of modal logics by using the internal
structure of categories of particular type (logos) was also
established. Category-theoretical constructs were hence used as
one of the possible semantic interpretations of intuitionistic
logic. This interpretation has also included intuionistic modal
logics using different semantical tools such as adjoint pair of
functors. In this paper, we discuss one of the possible
extension of intuitionistic logic.