Abstract
In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued Łukasiewicz logic \( \mathcal{L} \) ∞ to a suitable m-valued Łukasiewicz logic\( \mathcal{L} \) m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in \( \mathcal{L} \) ∞ if and only if it is also valid in \( \mathcal{L} \) m. We also reduce the notion of logical consequence in \( \mathcal{L} \) ∞ to the same notion in a suitable finite set of finite-valued Łukasiewicz logics. Finally, we define an analytic and internal sequent calculus for infinite-valued Łukasiewicz logic.
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Aguzzoli, S., Ciabattoni, A. Finiteness in Infinite-Valued Łukasiewicz Logic. Journal of Logic, Language and Information 9, 5–29 (2000). https://doi.org/10.1023/A:1008311022292
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DOI: https://doi.org/10.1023/A:1008311022292