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Integrating Linear Arithmetic into Superposition Calculus

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Computer Science Logic (CSL 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4646))

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Abstract

We present a method of integrating linear rational arithmetic into superposition calculus for first-order logic. One of our main results is completeness of the resulting calculus under some finiteness assumptions.

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References

  1. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University press, Cambridge (1998)

    Google Scholar 

  2. Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 1, pp. 19–100. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  3. Bachmair, L., Ganzinger, H., Waldmann, U.: Refutational Theorem Proving for Hierarchic First-Order Theories. Applicable Algebra in Engineering, Communication and Computing 5(3/4), 193–212 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Godoy, G., Nieuwenhuis, R.: Superposition with completely built-in Abelian groups. J. Symb. Comput. 37(1), 1–33 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hustadt, U., Motik, B., Sattler, U.: Reasoning in description logics with a concrete domain in the framework of resolution. In: ECAI, pp. 353–357 (2004)

    Google Scholar 

  6. Korovin, K., Voronkov, A.: Integrating linear arithmetic into superposition calculus. Journal version (in preparation)

    Google Scholar 

  7. Le Chenadec, P.: Canonical forms in finitely presented algebras. In: Research Notes in Theoretical Computer Science, Wiley, Chichester (1986)

    Google Scholar 

  8. Marché, C.: Normalized rewriting: An alternative to rewriting modulo a set of equations. J. Symb. Comput. 21(3), 253–288 (1996)

    Article  MATH  Google Scholar 

  9. Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, pp. 371–443. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  10. Rogers, H.: Theory of recursive functions and effective computability. MIT Press, Cambridge (1988)

    Google Scholar 

  11. Rubio, A., Nieuwenhuis, R.: A precedence-based total AC-compatible ordering. In: Kirchner, C. (ed.) Rewriting Techniques and Applications. LNCS, vol. 690, pp. 374–388. Springer, Heidelberg (1993)

    Google Scholar 

  12. Stuber, J.: Superposition theorem proving for Abelian groups represented as integer modules. Theor. Comput. Sci. 208(1-2), 149–177 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. Waldmann, U.: Superposition and chaining for totally ordered divisible Abelian groups. In: International Joint Conference for Automated Reasoning, pp. 226–241 (2001)

    Google Scholar 

  14. Waldmann, U.: Cancellative Abelian monoids and related structures in refutational theorem proving (part I, II). Journal of Symbolic Computation 33(6), 777–829 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Jacques Duparc Thomas A. Henzinger

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© 2007 Springer-Verlag Berlin Heidelberg

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Korovin, K., Voronkov, A. (2007). Integrating Linear Arithmetic into Superposition Calculus. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_19

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  • DOI: https://doi.org/10.1007/978-3-540-74915-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74914-1

  • Online ISBN: 978-3-540-74915-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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