Abstract
The first part of this chapter deals with disjunctive normal forms in the infinite-valued calculus of Łukasiewicz. We shall generalize the Farey-Schauder machinery of Chapter 3 to formulas in any number of variables. Disjunctive normal forms will be the key tool to prove Mc-Naughton’s theorem, generalizing the proof given in 3.2.8 for functions of one variable. We shall also discuss the relationships between normal form reductions and toric desingularizations, and the correspondence between MV-algebras and AF C*-algebras. Strengthening Corollary 4.5.3, we shall show that the tautology problem in the infinite-valued calculus is in fact co-NP-complete, thus having the same complexity as it boolean counterpart. We shall give a proof of Di Nola’s representation theorem for all MV-algebras.
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© 2000 Springer Science+Business Media Dordrecht
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Cignoli, R.L.O., D’Ottaviano, I.M.L., Mundici, D. (2000). Advanced topics. In: Algebraic Foundations of Many-Valued Reasoning. Trends in Logic, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9480-6_10
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DOI: https://doi.org/10.1007/978-94-015-9480-6_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5336-7
Online ISBN: 978-94-015-9480-6
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