A polyvalent propositional logic \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal L$\end{document} is in Boolean frame if the set of all \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal L$\end{document}-valid formulas coincides with the set of all tautologies. It is well known that the polyvalent logics based on the truth functionality principle are not in the Boolean frame. Interpolative Boolean logic (IBL) is a real-valued propositional logic that is in Boolean frame. The term “interpolative” cames from the fact that semantics of IBL is based on the notion of a generalized Boolean polynomial, where multiplication can be substituted by any continuous t-norm \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$*:0,1^2\longrightarrow 0,1$\end{document} such that \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$xy\leqslant x* y$\end{document}. Possible applications are illustrated with several examples.