In this survey paper we explore the connection between the Pierce- Birkhoff conjecture and Lukasiewicz logic with product. Conservative extensions of Lukasiewicz logic can be defined by adding an internal product or a multiplication with scalars from [0; 1]. The corresponding models reflect an algebraic hierarchy of lattice-ordered structures, from groups to algebras. We prove a general version of the normal form theorem and we state a local version of the Pierce-Birkhoff conjecture.

A General View on Normal Form Theorems for Łukasiewicz Logic with Product

Lapenta, Serafina;Leuştean, Ioana
2016

Abstract

In this survey paper we explore the connection between the Pierce- Birkhoff conjecture and Lukasiewicz logic with product. Conservative extensions of Lukasiewicz logic can be defined by adding an internal product or a multiplication with scalars from [0; 1]. The corresponding models reflect an algebraic hierarchy of lattice-ordered structures, from groups to algebras. We prove a general version of the normal form theorem and we state a local version of the Pierce-Birkhoff conjecture.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4708760
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