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We look at the complexity of the existence problem for a Horn sentence equivalent to a given one. It is proved that for a signature consisting of one unary function symbol and any finite number of unary predicate symbols, the problem is computable. For a signature with at least two unary function symbols, it is stated that the problem mentioned is an m-complete ∑10set\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\sum }_{1}^{0}\mathrm{set}$$\end{document}.
Algebra and Logic – Springer Journals
Published: Sep 1, 2022
Keywords: Horn formula; m-reducibility; ∑10set\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sum }_{1}^{0}\mathrm{set}$$\end{document}.
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