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Journal of Logic and Computation Advance Access originally published online on October 22, 2007
Journal of Logic and Computation 2008 18(1):35-57; doi:10.1093/logcom/exm053
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Analytic Calculi for Logics of Ordinal Multiples of Standard t-Norms

Thomas Vetterlein

European Centre for Soft Computing, Edificio Científico-Tecnológico, C/ Gonzalo Gutiérrez Quirós s/n, 33600 Mieres, Spain. E-mail: thomas.vetterlein{at}softcomputing.es

Received 29 May 2007.


  Abstract

For two propositional fuzzy logics, we present analytic proof calculi, based on relational hypersequents. The logic considered first, called ML, is based on the finite ordinal sums of Lukasiewicz t-norms. In addition to the usual connectives—the conjunction {odot}, the implication -> and the constant 0—we use a further unary connective interpreted by the function associating with each truth value a the greatest {odot}-idempotent below a. ML is a conservative extension of Basic Logic.

The second logic, called M{Pi}, is based on the finite ordinal sums of the product t-norm on (0, 1]. Our connectives are in this case just the conjunction and the implication.

Keywords: fuzzy logics; analytic calculi; Basic Logic


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