@InProceedings{10.1007/978-981-15-1342-8_1,
author="Flaminio, Tommaso
and Ugolini, Sara",
editor="Ju, Shier
and Palmigiano, Alessandra
and Ma, Minghui",
title="Hyperstates of Involutive MTL-Algebras that Satisfy $(2x)^2=2(x^2)$",
booktitle="Nonclassical Logics and Their Applications",
year="2020",
publisher="Springer Singapore",
address="Singapore",
pages="1--14",
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 {\$}{\$}{\backslash}ell {\$}{\$}-group.",
isbn="978-981-15-1342-8"
}