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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):577-601; doi:10.1093/jigpal/jzm054
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On Positive Relational Calculi

Renata de Freitas

Institute of Mathematics, UFF: Universidade Federal Fluminense; Niterói, Brazil. E-mail: naborges{at}cos.ufrj.br

Paulo A.S. Veloso

Systems and Computer Engin. Program, COPPE, UFRJ; Universidade Federal do Rio de Janeiro; Rio de Janeiro, Brazil. E-mail: veloso{at}cos.ufrj.br

Sheila R.M. Veloso

Systems and Computer Engin. Dept., Faculty of Engineering, UERJ: Universidade do Estado do Rio de Janeiro; Rio de Janeiro, Brazil. E-mail: srmv{at}bridge.com.br

Petrucio Viana

Institute of Mathematics, UFF: Universidade Federal Fluminense; Niterói, Brazil. E-mail: petrucio{at}cos.ufrj.br


  Abstract

We discuss the question of inclusions between positive relational terms and some of its aspects, using the form of a dialogue. Two possible approaches to the problem are emphasized: natural deduction and graph manipulations. Both provide sound and complete calculi for proving the valid inclusions, supporting nice strategies to obtain proofs in normal form, but the latter appears to present several advantages, which are discussed.

Key Words: Positive relational calculi • natural deduction • graph calculus • completeness • decidability.

Received for publication 25 April 2007.
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