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Logic Journal of IGPL Advance Access published online on October 12, 2007
Logic Journal of IGPL, doi:10.1093/jigpal/jzm046
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Restricted Classical Modal Logics

Cezar A. Mortari

Departamento de Filosofia, Universidade Federal de Santa Catarina, Trindade, 88040-900 Florianópolis, SC, Brazil, E-mail: cmortari{at}cfh.ufsc.br


  Abstract

We consider a family of noncongruential modal logics obtained by restricting the smallest classical modal logic E and some of its extensions. We show that these logics are also properly contained in Lemmon's S0.5; semantics for them are adapted from Cresswell's semantics for S0.5 and from neighborhood semantics for classical modal logics. Some extensions of these logics by means of usual modal logical axioms are also considered, and determination results proved. As a further example, we also show how to obtain restricted versions of some of Chellas and Segerberg's prenormal modal logics.

Key Words: modal logic • non-normal modal logics • noncongruential modal logics

Received for publication 15 September 2006.
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