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

Tommaso Flaminio; Sara Ugolini

doi:10.1007/978-981-15-1342-8_1

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arXiv · 2002.05587

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

Tommaso Flaminio·Sara Ugolini

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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 (IBP0-algebras for short). Grounding on a recent result showing that IBP0-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 IBP0- 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 l-group.

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BibTeX RIS

Tommaso Flaminio, Sara Ugolini. 2020-02-13. Hyperstates of Involutive MTL-Algebras that Satisfy $(2x)^2 = 2(x^2)$. https://doi.org/10.1007/978-981-15-1342-8_1

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