Logic Journal of IGPL Advance Access published online on September 3, 2009
Logic Journal of IGPL, doi:10.1093/jigpal/jzp041
On vague notions and modalities: a modular approach
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
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
Instituto de Matemática, Universidade Federal Fluminense.
E-mail: petrucio{at}cos.ufrj.br
Instituto de Matemática, Universidade Federal Fluminense.
E-mail: freitas{at}vm.uff.br
Instituto de Matemática, Universidade Federal do Rio de Janeiro.
E-mail: mario{at}cos.ufrj.br
Programa de Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro.
E-mail: carladelgado{at}gmail.com
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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