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System Description: aRa – An Automatic Theorem Prover for Relation Algebras

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Automated Deduction - CADE-17 (CADE 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1831))

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Abstract

aRa is an automatic theorem prover for various kinds of relation algebras. It is based on Gordeev’s Reduction Predicate Calculi for n-variable logic (RPC n ) which allow first-order finite variable proofs. Employing results from Tarski/Givant and Maddux we can prove validity in the theories of simple semi-associative relation algebras, relation algebras and representable relation algebras using the calculi RPC3 , RPC4 and RPC ω . aRa, our implementation in Haskell, offers different reduction strategies for RPC n , and a set of simplifications preserving n-variable provability.

This work was partially supported by DFG under grant Ku 966/4-1.

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References

  1. Chin, L.H., Tarski, A.: Distributive and modular laws in the arithmetic of relation algebras, vol. 1(9), pp. 341–384. University of California Publications in Mathematics, New Series, Berkeley, Los Angeles,santa barbara (1951)

    Google Scholar 

  2. J. Dawson and R. Gor_e. A mechanized proof system for relation algebra using display logic. In JELIA’98, LNAI 1489, pages 264{278. Springer, 1998.

    Chapter  Google Scholar 

  3. Gordeev, L.: Cut free formalization of logic with finitely many variables, part I. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 933, pp. 136–150. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  4. Gordeev, L.: Variable compactness in 1-order logic. Logic Journal of the IGPL 7(3), 327–357 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hattensperger, C., Berghammer, R., Schmidt, G.: RALF - a relationalgebraic formula manipulation system and proof checker. In: AMAST 1995, Workshops in Computing, pp. 405–406. Springer, Heidelberg (1994)

    Google Scholar 

  6. Maddux, R.: A sequent calculus for relation algebras. Annals of Pure and Applied Logic 25, 73–101 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  7. Tarski, A., Givant, S.: A Formalization of Set Theory without Variables. Optimization Techniques 1975, vol. 4. American Mathematical Society, Providence (1987)

    Google Scholar 

  8. von Oheimb, D., Gritzner, T.: RALL: Machine-supported proofs for relation algebra. In: McCune, W. (ed.) CADE 1997. LNCS(LNAI), vol. 1249, pp. 380–394. Springer, Heidelberg (1997)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Symbolic Computation Group, WSI for Computer Science, Universität Tübingen, D-72076, Tübingen, Germany

    Carsten Sinz

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  1. Carsten Sinz
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Editors and Affiliations

  1. Toyota Technological Institute at Chicago, 1427 E. 60th Street, 60637, Chicago, Illinois

    David McAllester

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© 2000 Springer-Verlag Berlin Heidelberg

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Sinz, C. (2000). System Description: aRa – An Automatic Theorem Prover for Relation Algebras. In: McAllester, D. (eds) Automated Deduction - CADE-17. CADE 2000. Lecture Notes in Computer Science(), vol 1831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721959_13

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  • DOI: https://doi.org/10.1007/10721959_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67664-5

  • Online ISBN: 978-3-540-45101-3

  • eBook Packages: Springer Book Archive

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