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Journal of Logic and Computation Advance Access published online on September 17, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp054
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Computing Minimal Axiomatizations in Gödel Propositional Logic

Stefano Aguzzoli

Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, via Comelico 39-41, 20135 Milano, Italy.
E-mail: aguzzoli{at}dsi.unimi.it

Ottavio M. D’Antona and Vincenzo Marra

Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, via Comelico 39-41, 20135 Milano, Italy.
E-mail: dantona{at}dico.unimi.it; marra{at}dico.unimi.it

Received 31 August 2008.


  Abstract

We solve the minimization problem for finitely axiomatizable theories in Gödel infinite-valued propositional logic. That is, we obtain an algorithm that when input a formula {alpha}(X1,...,Xn) outputs a formula β(X1,...,Xm) such that (i) the theories singly axiomatized by {{alpha}} and {β} have isomorphic algebraic semantics, and (ii) if β'(X1,...,Xm') is any formula satisfying (i), then m'≥m.

Keywords: Gödel propositional logic; minimal axiomatizations; normal forms


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