On the logical formalization of possibilistic counterparts of states over n-valued Łukasiewicz events
On the logical formalization of possibilistic counterparts of states over n-valued Łukasiewicz events
Possibility and necessity measures are commonly defined over Boolean algebras. This work considers a generalization of these kinds of measures over MV-algebras as a possibilistic counterpart of the (probabilistic) notion of state on MV-algebras. Two classes of possibilistic states over MV-algebras of functions are characterized in terms of (generalized) Sugeno integrals. For reasoning about these representable classes of possibilistic states, we introduce many-valued modal logics based on the Rational Łukasiewicz Logic, that are shown to be complete with respect to corresponding classes of Kripke models equipped with those states.
MV-algebras, generalized Sugeno integral, possibilistic states, Łukasiewicz logic
429-446
Flaminio, Tommaso
10824669-cfbb-4724-aa74-e1b31574dae8
Godo, Lluís
0518f088-84ec-4816-ad43-4e240ae66dc1
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
June 2011
Flaminio, Tommaso
10824669-cfbb-4724-aa74-e1b31574dae8
Godo, Lluís
0518f088-84ec-4816-ad43-4e240ae66dc1
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Flaminio, Tommaso, Godo, Lluís and Marchioni, Enrico
(2011)
On the logical formalization of possibilistic counterparts of states over n-valued Łukasiewicz events.
Journal of Logic and Computation, 21 (3), .
(doi:10.1093/logcom/exp012).
Abstract
Possibility and necessity measures are commonly defined over Boolean algebras. This work considers a generalization of these kinds of measures over MV-algebras as a possibilistic counterpart of the (probabilistic) notion of state on MV-algebras. Two classes of possibilistic states over MV-algebras of functions are characterized in terms of (generalized) Sugeno integrals. For reasoning about these representable classes of possibilistic states, we introduce many-valued modal logics based on the Rational Łukasiewicz Logic, that are shown to be complete with respect to corresponding classes of Kripke models equipped with those states.
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e-pub ahead of print date: 26 March 2009
Published date: June 2011
Keywords:
MV-algebras, generalized Sugeno integral, possibilistic states, Łukasiewicz logic
Identifiers
Local EPrints ID: 416724
URI: http://eprints.soton.ac.uk/id/eprint/416724
PURE UUID: 2f6bf907-0f02-4022-a06a-b3eab847886e
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Date deposited: 05 Jan 2018 17:30
Last modified: 15 Mar 2024 17:37
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Author:
Tommaso Flaminio
Author:
Lluís Godo
Author:
Enrico Marchioni
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