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Journal of Logic and Computation Advance Access published online on March 26, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp012
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

On the Logical Formalization of Possibilistic Counterparts of States over n-valued Lukasiewicz Events

Tommaso Flaminio

Dipartimento di Matematica e Informatica, Università degli Studi di Siena, Pian dei Mantellini 44, Siena, Italy.
E-mail: flaminio{at}unisi.it

Lluís Godo

Artificial Intelligence Research Institute (IIIA - CSIC), Campus UAB, Bellaterra 08193, Spain.
E-mail: godo{at}iiia.csic.es

Enrico Marchioni

Artificial Intelligence Research Institute (IIIA - CSIC), Campus UAB, Bellaterra 08193, Spain.
E-mail: enrico{at}iiia.csic.es

Received 6 October 2008.


  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 Lukasiewicz Logic, that are shown to be complete with respect to corresponding classes of Kripke models equipped with those states.

Keywords: possibilistic states; generalized Sugeno integral; Lukasiewicz logic; MV-algebras


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