Abstract
Since every MV-term τ is a string of symbols over a finite alphabet, one may naturally consider the following decision problem: does there exist an effective procedure (for definiteness, a Turing machine) deciding whether an arbitrary equation τ = 1 holds in all MV-algebras? More generally, given two terms σ and τ, does there exist an effective procedure to decide whether the McNaughton function determined by σ belongs to the principal ideal determined by τ in the free MValgebra Free ω ? These are respectively known as the word problem for free MV-algebras, and the word problem for finitely presented 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). Łukasiewicz ∞-valued calculus. In: Algebraic Foundations of Many-Valued Reasoning. Trends in Logic, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9480-6_5
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DOI: https://doi.org/10.1007/978-94-015-9480-6_5
Publisher Name: Springer, Dordrecht
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