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Logic Journal of IGPL Advance Access originally published online on October 12, 2007
Logic Journal of IGPL 2007 15(5-6):775-800; doi:10.1093/jigpal/jzm049
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Natural Deduction for ‘Generally’

Leonardo B. Vana and Paulo A. S. Veloso

Department of Systems and Computer Engineering, COPPE, Federal University of Rio de Janeiro (UFRJ) PO Box 68511, 21945-970, Rio de Janeiro, RJ, Brazil. E-mail: leobvana.veloso{at}cos.ufrj.br

Sheila R. M. Veloso

Department of Systems and Computer Engineering, State University of Rio de Janeiro (UERJ), Brazil. E-mail: srmv{at}bridge.com.br


  Abstract

Logics for ‘generally’ (LG’s) were introduced for handling assertions with vague notions (e.g. ‘generally’, ‘most’, ‘several’), which occur often in ordinary language and in science. LG’s provide a framework for distinct notions of ‘generally’: one builds a specific logic for the notion one has in mind. We introduce deductive systems, in natural deduction style, for LG’s and show that these systems are normalizable.

Key Words: Logics of ‘generally’ • natural deduction • normalization • generalized quantifiers • vague notions.

Received for publication 25 September 2006.
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