General form of α-resolution principle for linguistic truth-valued lattice-valued logic

This paper is focused on resolution-based automated reasoning theory in linguistic truth-valued lattice-valued logic based on linguistic truth-valued lattice implication algebra. Concretely, the general form of α-resolution principle based on the above lattice-valued logic is equivalently transformed into another simpler lattice-valued logic system. Firstly, the general form of α-resolution principle for lattice-valued propositional logic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ({\fancyscript{L}}_{n} \times {\fancyscript{L}}_{2}){\text{P(X)}} $$\end{document} is equivalently transformed into that for lattice-valued propositional logic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \fancyscript{L}_{n} $$\end{document}P(X). A similar conclusion is obtained between the general form of α-resolution principle for linguistic truth-valued lattice-valued propositional logic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{L}}_{V(n \times 2)}$$\end{document}P(X) and that for lattice-valued propositional logic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{L}}_{Vn} $$\end{document}P(X). Secondly, the general form of α-resolution principle for lattice-valued first-order logic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ({\fancyscript{L}}_{n} \times {\fancyscript{L}}_{2}) $$\end{document}F(X) is equivalently transformed into that for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{L}}_{n} $$\end{document}P(X). Similarly, this conclusion also holds for linguistic truth-valued lattice-valued first-order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{L}}_{V(n \times 2)} $$\end{document}F(X) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{L}}_{Vn} $$\end{document}P(X). The presented work provides a key theoretical support for automated reasoning approaches and algorithms in linguistic truth-valued logic, which can further support linguistic information processing for decision making, i.e., reasoning with words.