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.
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Flaminio, T., Ugolini, S. (2020). Hyperstates of Involutive MTL-Algebras that Satisfy \((2x)^2=2(x^2)\). In: Ju, S., Palmigiano, A., Ma, M. (eds) Nonclassical Logics and Their Applications. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-15-1342-8_1
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