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1 2006

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Finitely equivalential Gentzen systems and the reduced matrices of the Gentzen systems associated with finitely valued logics

Gil A. J., Rebagliato J.

Reports on Mathematical Logic

2006

Nr 41,spec. iss.

9-30

uent calculus satisfying the cut elimination prop- erty and from which it is possible to dene all nitely valued logics determined by a matrix on the algebra. In this paper we study some algebraic properties of these sequent calculi. Our starting point is the denition of a Gentzen system as the consequence rela- tion determined by a sequent calculus over the set of (many-sided) sequents. For the Gentzen systems associated with an arbitrary - nite algebra we characterize the algebraic reducts of their reduced matrices as the quasivariety generated by the algebra. To prove this result we dene and study the basic properties of the nitely equivalential Gentzen systems. Throughout the paper dierent re- sults illustrate how to bridge the gap between the proof-theoretical and the algebraic properties of a sequent calculus.