The University of Southampton
University of Southampton Institutional Repository

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.

This record has no associated files available for download.

More information

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

Catalogue record

Date deposited: 05 Jan 2018 17:30
Last modified: 15 Mar 2024 17:37

Export record

Altmetrics

Contributors

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

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×