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Conference in Algebra (in honour of the 70th birthday of Ervin Fried)
August 17-21, 1999
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
Budapest, Hungary

Organizers
László Márki

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Algebra and Logic: Ideal Theory and Natural Deduction
by
Aldo Ursini
Department of Mathematics, University of Siena, Siena, Italy

It is shown how to give an algebraic formulation of logical systems presented by natural deduction rules. This is done in the frameworkk of subtractive algebras, and the main tool is the notion of 1-ideal. This allows for a variant of the Curry-Howard isomorphism in which terms are algebraic terms (as opposed to Lambda-terms) and proofs are equational proofs. The normalization of deductions will correspond to a normalization of algebraic terms.

Date received: June 17, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadj-10.