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States on commutative basic algebras
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DOI：10.1016/j.fss.2011.07.010.png)
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Abstract
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The paper deals with states on commutative basic algebras that are a non-associative generalization of MV-algebras or, in other words, the algebraic semantics for a fuzzy logic which generalizes the Lukasiewicz logic in that the conjunction is not associative. States are defined in the same way as Mundici's states on MV-algebras as normalized finitely additive [0,1]-valued functions, and sonic results analogous to the results that are known from MV-algebras are proved. (C) 2011 Elsevier B.V. All rights reserved.
Keywords:
Commutative basic algebra
MV-algebra
Representability
Ideal
MV-ideal
State
State-morphism
De Finetti's coherence criterion
Journal
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2.7
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7.6K
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1.5W