We introduce a generalised notion of state as an additive map from a Boolean algebra of events to an arbitrary MV-algebra. Generalised states become unary operations in two-sorted algebraic structures that we call state algebras. Since these, as we show, form an equationally defined class of algebras, universal-algebraic techniques apply. We discuss free state algebras, their geometric representation, and their connection with the theory of affine representations of lattice groups.
Generalised states : a multi-sorted algebraic approach to probability / T. Kroupa, V. Marra. - In: SOFT COMPUTING. - ISSN 1432-7643. - 21:1 (Special Issue)(2017 Jan), pp. 57-67. [10.1007/s00500-016-2343-3]
Generalised states : a multi-sorted algebraic approach to probability
T. Kroupa
;V. MarraUltimo
2017
Abstract
We introduce a generalised notion of state as an additive map from a Boolean algebra of events to an arbitrary MV-algebra. Generalised states become unary operations in two-sorted algebraic structures that we call state algebras. Since these, as we show, form an equationally defined class of algebras, universal-algebraic techniques apply. We discuss free state algebras, their geometric representation, and their connection with the theory of affine representations of lattice groups.File | Dimensione | Formato | |
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