Skip to main content

Decision problems for tarski and presburger arithmetics extended with sets

  • Conference paper
  • First Online:
Computer Science Logic (CSL 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 533))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W.W. Bledsoe. Non-resolution theorem proving. J. Art. Int., 9:1–35, 1977.

    Article  Google Scholar 

  2. W.W. Bledsoe. Some automatic proof in analysis. Contemporary AMS editor, Automated Theorem Proving after 25 years, 1984.

    Google Scholar 

  3. D. Cantone, A. Ferro, and E.G. Omodeo. Computable Set Theory. Oxford University Press, 1990.

    Google Scholar 

  4. D. Cantone, A. Ferro, E. Omodeo, and J.T. Schwartz. Decision algorithms for some fragments of Analysis and related areas. Comm. Pure App. Math., XL:281–300, 1987.

    Google Scholar 

  5. D. Cantone and E. Omodeo. On the decidability of formulae involving continuous and closed functions. In N.S. Sridharam, editor, Eleventh Int. Joint Conf. on Art. Intell., pages 425–430, 1989.

    Google Scholar 

  6. D. Cantone and E. Omodeo. Topological syllogistic with continuous and closed functions. Comm. Pure App. Math., XLII, n. 8:1175–1188, 1989.

    Google Scholar 

  7. G.E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Proc. 2nd GI Conf. Automata Theory and Formal Languages. Springer Lecture Notes in CS, 33:134–183, 1975.

    Google Scholar 

  8. D. Cantone, E. Omodeo, and A. Policriti. The automation of syllogistic. II. Optimisation and complexity issues. Journal of Automated Reasoning, 6:173–187, 1990.

    Article  Google Scholar 

  9. J.H. Davenport and J. Heintz. Real quantifier elimination is doubly exponential. J. Symb. Comp., 5:29–35, 1988.

    Google Scholar 

  10. J.H. Davenport, Y. Siret, and E. Tournier. Computer Algebra. Systems and algorithms for algebraic computation. Academic Press Limited, 1988.

    Google Scholar 

  11. A. Ferro and E. Omodeo. Decision procedures for elementary sublanguages of set theory. VII. validity in set theory when a choice operator is present. Comm. Pure App. Math., XL:265–280, 1987.

    Google Scholar 

  12. A. Ferro, E. Omodeo, and J.T. Schwartz. Decision procedures for elementary sublanguages of set theory. I. Multilevel syllogistic and some extensions. Comm. Pure App. Math., XXXIII:599–608, 1980.

    Google Scholar 

  13. R.S. Garfinkel and G.L. Nemhauser. Integer programming. John Wiley & Sons, Inc., New York, 1972.

    Google Scholar 

  14. Y. Matijasevič. Enumerable sets are Diophantine sets. Soviet Math. Doklady, 11:354–357, 1970.

    Google Scholar 

  15. E.G. Omodeo. Decidability and proof procedures for set theory with a choice operator. PhD thesis, New York University, 1984.

    Google Scholar 

  16. C.H. Papadimitriou. On the complexity of Integer Programming. Journal of ACM, 28, N. 4:765–768, 1981.

    Article  Google Scholar 

  17. F. Parlamento and A. Policriti. Decision procedures for elementary sublanguages of set theory. XIII. Model graphs, reflection and decidability. To appear in J. Automated Reasoning, 1990.

    Google Scholar 

  18. M. Presburger. Über die Vollständigkeit eines gewissen Systems der Arithmetic ganzer Zahlen, in welchem die Addition als einsige Operation hervortritt. In Comptes-rendus du Premier Congrès des Mathematiciens des Pays Slaves, pages 192–201,395. Warsaw, 1929.

    Google Scholar 

  19. H.M. Salkin. Integer programming. Addison-Wesley Publishing Co., Inc., Reading, Mass., 1975.

    Google Scholar 

  20. A. Tarski. A decision method for elementary algebra and geometry. Univ. of California Press, Berkeley, 2nd ed. rev., 1951.

    Google Scholar 

  21. A. Tarski. What is elementary geometry? In L. Henkin, P. Suppes, and A. Tarski, editors, The axiomatic method with special reference to geometry and physics, pages 16–29, 1959.

    Google Scholar 

  22. V. Weispfenning. The complexity of linear problems in fields. J. Symb. Comp., 5:3–28, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Egon Börger Hans Kleine Büning Michael M. Richter Wolfgang Schönfeld

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cantone, D., Cutello, V., Schwartz, J.T. (1991). Decision problems for tarski and presburger arithmetics extended with sets. In: Börger, E., Kleine Büning, H., Richter, M.M., Schönfeld, W. (eds) Computer Science Logic. CSL 1990. Lecture Notes in Computer Science, vol 533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54487-9_54

Download citation

  • DOI: https://doi.org/10.1007/3-540-54487-9_54

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54487-6

  • Online ISBN: 978-3-540-38401-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics