Abstract

We consider a syntax and semantics of modal logics based on parametrized modal connectives with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\exists \forall $$\end{document}-satisfaction definitions, we axiomatically introduce different parametrized modal logics, we prove their completeness with respect to appropriate classes of parametrized relational structures and we show the decidability of some related satisfiability problems.