Superintuitionistic logics are obtained from intuitionistic logic by including additional axioms. The major goal of the present work is to develop proof methods of irresolvability for various properties of superintuitionistic logics and of some related fragments of modal logics. The article presents three levels of application for these methods. Previously known and newly obtained results of property irresolvability for superintuitionistic and modal logics are grouped into a table with 38 rows (properties) and 8 columns (logics).

superintuitionistic logic, intuitionistic logic, modal logic, axioms, irresolvability, Kripke scales

Mathematical problems and theory of numerical methods