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Hyperstates of Involutive MTL-Algebras that Satisfy \((2x)^2=2(x^2)\)

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Part of the Logic in Asia: Studia Logica Library book series (LIAA)

Abstract

States of MV-algebras have been the object of intensive study and attempts of generalizations. The aim of this contribution is to provide a preliminary investigation for states of prelinear semihoops and hyperstates of algebras in the variety generated by perfect and involutive MTL-algebras (IBP\(_0\)-algebras for short). Grounding on a recent result showing that IBP\(_0\)-algebras can be constructed from a Boolean algebra, a prelinear semihoop and a suitably defined operator between them, our first investigation on states of prelinear semihoops will support and justify the notion of hyperstate for IBP\(_0\)-algebras and will actually show that each such map can be represented by a probability measure on its Boolean skeleton, and a state on a suitably defined abelian \(\ell \)-group.

Keywords

IBP\(_0\)-algebras Abelian \(\ell \)-groups Prelinear semihoop States of prelinear semihoop Hyperstates 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.IIIA - CSIC, Campus de la Universidad Autònoma de Barcelona S/nBellaterraSpain
  2. 2.Department of Computer ScienceUniversity of PisaPisaItaly

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