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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

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.

References

  1. Andréka H. Representations of distributive lattice-ordered semigroups with binary relations. Algebra Univers (1991) 28:12–25.[CrossRef]

  2. Frias M, Veloso P, Baum G. Fork algebras: past, present and future. Journal of Relational Methods in Computer Science (2004) 1:181–216.

  3. Lyndon R. The representation of relational algebras. Annals Math (1950) 51:707–729.[CrossRef]

  4. Lyndon R. The representation of relational algebras II. Annals Math (1956) 63:294–307.[CrossRef]

  5. Maddux RD. A sequent calculus for relation algebras. Annals of Pure and Applied Logic (1983) 25:73–101.[CrossRef][ISI]

  6. Maddux RD. Relation-algebraic semantics. Theoretical Computer Science (1996) 160:1–85.[CrossRef][ISI]

  7. Monk JD. Non-finitizability of classes of representable cylindric algebras. Journal of Symbolic Logic (1969) 34:331–343.[CrossRef][ISI]

  8. Prawitz D. Natural Deduction, A Proof Theoretic Study. (1965) Stockholm: Almqvist and Wiksell.

  9. Schein B. Relation algebras and function semigroups. Semigroup Forum (1970) 1:1–62.[CrossRef]

  10. Tarski A. On the calculus of relations. Journal of Symbolic Logic (1941) 6:73–89.[CrossRef]

  11. van Dalen D. Logic and Structure. (2004) 4th edition. Berlin: Springer-Verlag.

  12. Viana P. Non-logical Extensions of the Relational Calculus. (2005) D.Sc. thesis, Systems and Computer Engineering Program, COPPE, Universidade Federal do Rio de Janeiro.

  13. de Freitas RP, Veloso PAS, Veloso SRM, Viana P. Reasoning with graphs. Electronic Notes in Theoretical Computer Science—Mints G, de Queiroz R, eds. (2006) 165. Proceedings of the 13th Workshop on Logic, Language, Information and Computation (WoLLIC 2006). 201–212.[CrossRef]

  14. Wadge W. A complete natural deduction system for the relation calculus. Theory of Computation Report (1975) 5, University of Warwick.


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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
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Right arrow Articles by de Freitas, R.
Right arrow Articles by Viana, P.
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Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?