We construct a class of Lukasiewicz formulae whose associated McNaughton functions constitute a family of Schauder hats having special properties. Our technique is inspired by the well-known algorithm of Brun [3,4,2] for simultaneous diopanthine approximations. As a first application of Brun hats we construct normal forms for co-atomic Lukasiewicz logics. We also show how to combine Brun hats to obtain normal forms for all finite-valued Lukasiewicz logics.
Brun normal forms for co-atomic Lukasiewicz logics / S. Aguzzoli, O.M. D'Antona, V. Marra - In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 8th European Conference, ECSQARU 2005 : Barcelona, Spain, July 6-8, 2005 : Proceedings / Lluis Godo. - Berlin : Springer, 2005. - ISBN 3540273263. - pp. 650-661 (( Intervento presentato al 8th. convegno European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty: tenutosi a Barcellona, Spagna nel 2005.
Brun normal forms for co-atomic Lukasiewicz logics
S. AguzzoliPrimo
;O.M. D'AntonaSecondo
;V. MarraUltimo
2005
Abstract
We construct a class of Lukasiewicz formulae whose associated McNaughton functions constitute a family of Schauder hats having special properties. Our technique is inspired by the well-known algorithm of Brun [3,4,2] for simultaneous diopanthine approximations. As a first application of Brun hats we construct normal forms for co-atomic Lukasiewicz logics. We also show how to combine Brun hats to obtain normal forms for all finite-valued Lukasiewicz logics.
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