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Logic Journal of IGPL Advance Access published online on September 3, 2009
Logic Journal of IGPL, doi:10.1093/jigpal/jzp041
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On vague notions and modalities: a modular approach

Paulo A. S. Veloso

Programa de Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970, Rio de Janeiro, RJ, Brasil.
E-mail: veloso{at}cos.ufrj.br

Sheila R. M. Veloso

Departamento de Engenharia de Sistemas e Computação, Faculdade de Engenharia de Sistemas e Computação, Universidade Estadual do Rio de Janeiro.
E-mail: sheila{at}cos.ufrj.br

Petrucio Viana

Instituto de Matemática, Universidade Federal Fluminense.
E-mail: petrucio{at}cos.ufrj.br

Renata De Freitas

Instituto de Matemática, Universidade Federal Fluminense.
E-mail: freitas{at}vm.uff.br

Mario Benevides

Instituto de Matemática, Universidade Federal do Rio de Janeiro.
E-mail: mario{at}cos.ufrj.br

Carla Delgado

Programa de Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro.
E-mail: carladelgado{at}gmail.com


  Abstract

Vague notions, such as ‘generally’, ‘rarely’, ‘often’, ‘almost always’, ‘a meaningful subset of a whole’, ‘most’, etc., occur often in ordinary language and in some branches of science. We introduce modal logical systems, with generalized operators, for the precise treatment of assertions involving some versions of such vague notions. We examine modal logics, constructed in a modular fashion, with generalized operators corresponding to some versions of ‘generally’ and ‘rarely’.

Key Words: Modal logic • vague notions • generally • rarely • knowledge representation

Received for publication 21 July 2009.
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