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S. Buss (1998)
Chapter I - An Introduction to Proof TheoryStudies in logic and the foundations of mathematics, 137
Alexander Borgida, Enrico Franconi, Ian Horrocks, D. McGuinness, P. Patel-Schneider (2000)
Explaining ALC Subsumption
J. Avigad (2017)
Proof Theory
[In this chapter, we present our first deduction system for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{ ALC} $$\end{document}, a Sequent Calculus for ACL named \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ SC} _{\mathcal{ ALC} }$$\end{document}. This first system is a labeled style proof system pure propositional in a sense that we don’t deal with variables or individuals. Besides presenting the system, we also present the main proof theoretical properties of it. That is, we proof that the system is complete, sound and its cut rule can be removed without compromising its completeness.]
Published: May 17, 2012
Keywords: Sequent calculus; Completeness theorem; Soundness theorem; Cut-elimination; Gentzen’s Hauptsatz
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