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Journal of Logic and Computation, Volume 10, Issue 2, pp. 213-222: Abstract.

Sequent calculi for finite-valued Lukasiewicz logics via Boolean decompositions

S Aguzzoli1, A Ciabattoni2 and A Di Nola3

1Dipartimento di Matematica, University of Siena, Via Del Capitano, 15, Siena, Italy, E-mail: aguzzoli@unist.it, 2Dipartimento di Informatica, University of Milano, Via Comelico, 39, Milano, Italy, E-mail: ciabatto@dsi.unimi.it, 3Dipartimento di Informatica ed Applicazioni, University of Salerno, Baronissi, Italy, E-mail: dinola@unina.it

In this paper we define internal cut-free sequent calculi for any n-valued Lukasiewicz logic Ln. These calculi are based on a representation of formulas of Ln, by n - 1 many {0, 1}-valued formulas of Ln. They enjoy the usual properties of sequent systems like symmetry, subformula property and invertibility of the rules. Upon dualizing our calculi one obtains Hähnle's tableau systems. Then they provide a reformulation of Hähnle's approach to theorem proving that makes no use of nonlogical elements.

Keywords: Many-valued logics, Lukasiewicz logic, sequent calculus.

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