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Journal of Logic and Computation 1997 7(4):473-500; doi:10.1093/logcom/7.4.473
© 1997 by Oxford University Press
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Original Articles

On Gentzen Systems Associated with the Finite Linear MV-algebras

ÀNGEL J. GIL, ANTONI TORRENS and VENTURA VERDÚ

Universitat Pompeu Fabra Barcelona, Spain E-mail: gil_angel{at}empr.upf.es
Universitat de Barcelona Barcelona, Spain E-mail: torrens{at}cerber.mat.ub.es
Universitat de Barcelona Barcelona, Spain E-mail: verdu{at}cerber.mat.ub.es

In this paper we obtain a characterization of the algebraizability of an m-dimensional Gentzen system in line with the characterization obtained for m-dimensional deductive systems and the characterization of 2-dimensional Gentzen systems. We also prove that if S(m) is the finite linear MV-algebraof m elements, then the m-dimensional Gentzen system obtained by using the sequent calculi associated with S(m) is equivalent to the m-valued Lukasiewicz logic Lm and to the equational consequence relation associated with S(m). Taking the two-element Boolean algebra we obtain the expected result concerning the relationship between the sequent calculus LK, the Classical Prepositional Calculus and the variety of Boolean algebras.

Keywords: Gentzen system; MV-algebras; deductive system; \ukasiewicz logic; sequent calculus.


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