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Título

Towards a probability theory for product logic: States, integral representation and reasoning

AutorFlaminio, Tommaso ; Godo, Lluis ; Ugolini, Sara
Palabras claveProbability theory
Two-tiered modal logics
Regular Borel measures
Nonclassical events
Free product algebras
States
Fecha de publicación2018
EditorElsevier
CitaciónInternational Journal of Approximate Reasoning 93: 199- 218 (2018)
ResumenThe aim of this paper is to extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called state, and show that every state is the Lebesgue integral with respect to a unique regular Borel probability measure. Furthermore, the relation between states and measures is shown to be one–one. In addition, we study geometrical properties of the convex set of states and show that extremal states, i.e., the extremal points of the state space, are the same as the truth-value assignments of the logic. Finally, we axiomatize a two-tiered modal logic for probabilistic reasoning on product logic events and prove soundness and completeness with respect to probabilistic spaces, where the algebra is a free product algebra and the measure is a state in the above sense. © 2017 Elsevier Inc.
URIhttp://hdl.handle.net/10261/161341
Identificadoresdoi: 10.1016/j.ijar.2017.11.003
issn: 0888-613X
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