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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
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
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), 429-446. (doi:10.1093/logcom/exp012).

Record type: Article

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

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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: 11 Aug 2021 16:30

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Contributors

Author: Tommaso Flaminio
Author: Lluís Godo
Author: Enrico Marchioni

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