Studia Logica

, Volume 71, Issue 2, pp 177–198 | Cite as

Complexity and Nicety of Fluted Logic

  • William C. Purdy


Fluted Logic is essentially first-order predicate logic deprived of variables. The lack of variables results in reduced expressiveness. Nevertheless, many logical problems that can be stated in natural language, such as the famous Schubert's Steamroller, can be rendered in fluted logic. Further evidence of the expressiveness of fluted logic is its close relation to description logics. Already it has been shown that fluted logic is decidable and has the finite-model property. This paper shows that fluted logic has the exponential-model property and that deciding satisfiability is NEXPTIME-complete. It is shown further that fluted logic is 'nice’, that is, it shares with first-order predicate logic the interpolation property and model preservation properties.

fluted logic first-order fragment complexity interpolation property preservation properties 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Andréka, Hajnal, Johan van Benthem, and Istvan Németi, 'Modal languages and bounded fragments of predicate logic', Journal of Philosophical Logic 27 (1998), 217-274.Google Scholar
  2. [2]
    Andréka, Hajnal, Ágnes Kurucz, István Németi, and Ildikó Sain, Applying Algebraic Logic; A General Methodology Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary, 1994.Google Scholar
  3. [3]
    Andrews, Peter B., An Introduction to Mathematical Logic and Type Theory, Academic Press, Orlando, 1986.Google Scholar
  4. [4]
    van Benthem, Johan, Exploring Logical Dynamics, CLSI Publications, Stanford, California, 1996.Google Scholar
  5. [5]
    Grädel, E., P. Kolaitis, and M. Vardi, 'On the decision problem for two-variable first-order logic', Bulletin of Symbolic Logic 3 (1997), 53-69.Google Scholar
  6. [6]
    Halpern, Joseph Y., and Yoram Moses, 'A guide to completeness and complexity for modal logics of knowledge and belief', Artificial Intelligence 54 (1992), 319-379.Google Scholar
  7. [7]
    Hintikka, Jaakko, 'Surface information and depth information', in J. Hintikka, and P. Suppes (eds.), Information and Inference, D. Reidel Publishing Company, Dordrecht, 1970, pp. 263-297.Google Scholar
  8. [8]
    Hintikka, Jaakko, Logic, Language-Games and Information, Clarendon Press, Oxford, 1973.Google Scholar
  9. [9]
    Hoogland, Eva, and Maarten Marx, 'Interpolation in Guarded Fragments', ILLC preprint, University of Amsterdam, 2000.Google Scholar
  10. [10]
    Hustadt, U., and R. A. Schmidt, 'Issues of decidability for description logics in the framework of resolution', in R. Caferra and G. Salzer (eds), Automated Deduction in Classical and Non-Classical Logic, Lecture Notes in Artificial Intelligence, 1761, Springer, New York, 2000, pp. 191-205.Google Scholar
  11. [11]
    Lutz, Carsten and Ulrike Sattler, 'The complexity of reasoning with Boolean modal logics', LTCS-Report 00-02, Aachen University of Technology, Aachen, 2000.Google Scholar
  12. [12]
    Hans Jürgen Ohlbach and Renate A. Schmidt, 'Functional translation and second-order frame properties of modal logics', Journal of Logic and Computation 7, 1997, 581-603.Google Scholar
  13. [13]
    Purdy, W. C., 'Fluted formulas and the limits of decidability', Journal of Symbolic Logic 61 (1996), 608-620. This as well as other papers by the author cited here can be obtained by ftp from wcpurdy/.Google Scholar
  14. [14]
    Purdy, W. C., 'Quine's “Limits of Decision”', Journal of Symbolic Logic 64 (1999), 1439-1466.Google Scholar
  15. [15]
    Rantala, Veikko, 'Constituents', in J. Bogdan Radu (ed.), Jaakko Hintikka, D. Reidel Publishing Company, Dordrecht, 1987, pp. 43-76.Google Scholar
  16. [16]
    Schmidt, R. A., 'Decidability by resolution for propositional modal logics', Journal of Automated Reasoning 22, 1999, 379-396.Google Scholar
  17. [17]
    Schmidt, R. A., and U. Hustadt, 'A resolution decision procedure for fluted logic', in D. McAllester (ed.), Automated Deduction-CADE-17, Lecture Notes in Artificial Intelligence 1831, Springer, New York, 2000, pp. 433-448.Google Scholar
  18. [18]
    Smullyan, Raymond M., First-Order Logic, Dover Publications, New York, 1995.Google Scholar
  19. [19]
    Stickel, Mark E., 'Schubert's steamroller problem: Formulations and solutions', Journal of Automated Reasoning 2 (1986), 89-101.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • William C. Purdy
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceSyracuse UniversitySyracuse

Personalised recommendations