Analytic calculi for logics of ordinal multiples of standard t-norms

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Authors:
Thomas Vetterlein
Title: Analytic calculi for logics of ordinal multiples of standard t-norms
Journal: Journal of Logic and Computation
Volume 18
Number
Pages: 35 - 57
Year: 2008





Abstract

We define the logic ML - the logic of finite ordinal sums of Lukasiewicz t-norms. In addition to the conjunction, implication, and 0 constant, we use the "storage" connective, interpreted by the function associating to every truth value the largest idempotent below it. ML is a conservative extension of BL. For ML, we define an r-hypersequent calculus, where the rules introducing the conjunction and implication are invertible. The aim of this paper is to provide an indirect solution to the problem how to define an analytic calculus for BL.