caa a22 4500 475800087 CHVBK 20180406123735.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1023/A:1008311022292 doi (NATIONALLICENCE)springer-10.1023/A:1008311022292 Finiteness in Infinite-Valued Łukasiewicz Logic [Elektronische Daten] [Stefano Aguzzoli, Agata Ciabattoni] 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. Kluwer Academic Publishers, 2000 analytic sequent calculus nationallicence infinite-valued Łukasiewicz logic nationallicence many-valued logic nationallicence McNaughton's theorem nationallicence Aguzzoli Stefano Dipartimento di Matematica, University of Siena, Via Del Capitano 15, Siena, Italy aut Ciabattoni Agata Dipartimento di Informatica, University of Milano, Via Comelico 39, Milan, Italy aut Journal of Logic, Language and Information Kluwer Academic Publishers 9/1(2000-01-01), 5-29 0925-8531 9:1<5 2000 9 10849 https://doi.org/10.1023/A:1008311022292 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008311022292 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aguzzoli Stefano Dipartimento di Matematica, University of Siena, Via Del Capitano 15, Siena, Italy aut NATIONALLICENCE 700 1- Ciabattoni Agata Dipartimento di Informatica, University of Milano, Via Comelico 39, Milan, Italy aut NATIONALLICENCE 773 0- Journal of Logic, Language and Information Kluwer Academic Publishers 9/1(2000-01-01), 5-29 0925-8531 9:1<5 2000 9 10849 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer