Journal of Automated Reasoning

, Volume 47, Issue 2, pp 111–132

Automated Inference of Finite Unsatisfiability

Article

Abstract

We present Infinox, an automated tool for analyzing first-order logic problems, aimed at showing finite unsatisfiability, i.e., the absence of models with finite domains. Finite satisfiability is not a decidable problem (only semi-decidable), which means that such a tool can never be complete. Nonetheless, our hope is that Infinox be a useful complement to finite model finders in practice. Infinox uses several different proof techniques for showing infinity of a set, each of which requires the identification of a function or a relation with particular properties. Infinox enumerates candidates to such functions and relations, and subsequently uses an automated theorem prover as a sub-procedure to try to prove the resulting proof obligations. We have evaluated Infinox on the relevant problems from the TPTP benchmark suite, and we are able to automatically show finite unsatisfiability for over 25% of these problems.

Keywords

Finite unsatisfiability Automated theorem proving Automated reasoning 

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References

  1. 1.
    Benzmüller, C., Theiss, F., Paulson, L., Fietzke, A.: LEO-II—a cooperative automatic theorem prover for higher-order logic. In: Automated Reasoning, 4th International Joint Conference, IJCAR 2008, Sydney, Australia, 12–15 August, 2008, Proceedings. LNCS, vol. 5195, pp. 162–170. Springer (2008)Google Scholar
  2. 2.
    Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Universitext. Springer (2001)Google Scholar
  3. 3.
    Claessen, K., Lillieström, A.: Automated inference of finite unsatisfiability. In: CADE-22: Proceedings of the 22nd International Conference on Automated Deduction, pp. 388–403. Springer, Berlin, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Claessen, K., Sörensson, N.: New techniques that improve MACE-style model finding. In: Proc. of Workshop on Model Computation (MODEL) (2003)Google Scholar
  5. 5.
    Curry, H.B.: Foundations of Mathematical Logic. Courier Dover Publications (1977)Google Scholar
  6. 6.
    McCune, W.: Solution of the Robbins problem. J. Autom. Reas. 19(3), 263–276 (1997)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    McCune, W.: Mace4 reference manual and guide. CoRR, cs.SC/0310055 (2003)Google Scholar
  8. 8.
    Roederer, A., Puzis, Y., Sutcliffe, G.: Divvy: an ATP meta-system based on axiom relevance ordering. In: CADE, pp. 157–162 (2009)Google Scholar
  9. 9.
    Schulz, S.: E—a brainiac theorem prover. AI Commun. 15(2, 3), 111–126 (2002)MATHGoogle Scholar
  10. 10.
    Sutcliffe, G.: The SZS ontologies for automated reasoning software. In: Rudnicki, P., Sutcliffe, G., Konev, B., Schmidt, R.A., Schulz, S. (eds.) LPAR Workshops. CEUR Workshop Proceedings, vol. 418. CEUR-WS.org (2008)
  11. 11.
    Sutcliffe, G.: The TPTP problem library and associated infrastructure: the FOF and CNF parts, v3.5.0. J. Autom. Reas. 43(4), 337–362 (2009)MATHCrossRefGoogle Scholar
  12. 12.
    Sutcliffe, G., Suttner, C.: The state of CASC. AI Commun. 19(1), 35–48 (2006)MATHMathSciNetGoogle Scholar
  13. 13.
    Vännännen, J.: A Short Course on Finite Model Theory. Department of Mathematics, University of Helsinki (2006)Google Scholar
  14. 14.
    Weidenbach, C., Brahm, U., Hillenbrand, T., Keen, E., Theobalt, C., Topić, D.: SPASS version 2.0. In: Voronkov, A. (ed.) Automated Deduction, CADE-18: 18th International Conference on Automated Deduction. Lecture Notes in Artificial Intelligence, vol. 2392, pp. 275–279. Springer, Copenhagen, Denmark (2002)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Chalmers University of TechnologyGothenburgSweden

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