Is It Reasonable to Employ Agents in Automated Theorem Proving?

Max Wisniewski, Christoph Benzmüller

Abstract

Agent architectures and parallelization are, with a few exceptions, rarely to encounter in traditional automated theorem proving systems. This situation is motivating our ongoing work in the higher-order theorem prover Leo-III . In contrast to its predecessor – the well established prover LEO-II – and most other modern provers, Leo-III is designed from the very beginning for concurrent proof search. The prover features a multiagent blackboard architecture for reasoning agents to cooperate and to parallelize proof construction on the term, clause and search level.

References

  1. Bachmair, L. and Ganzinger, H. (1994). Rewrite-based equational theorem proving with selection and simplification. J. Log. Comp., 4(3):217-247.
  2. Bellifemine, Fabio and Rimassa, Giovanni (2001), Developing Multi-agent Systems with a FIPA-compliant Agent Framework. J. Softw. Pract. Exper., 31, pages 103-128, John Wiley & Sons.
  3. Benzmüller, C. (1999). Extensional higher-order paramodulation and RUE-resolution. In CADE, number 1632 in LNCS, pages 399-413. Springer.
  4. Benzmüller, C. and Kohlhase, M. (1998). LEO - a higherorder theorem prover. In CADE, number 1421 in LNCS, pages 139-143. Springer.
  5. Benzmüller, C. and Miller, D. (2014). Automation of higher-order logic. In Siekmann, J., Gabbay, D., and Woods, J., eds., Handbook of the History of Logic, Vol. 9 - Logic and Computation . Elsevier.
  6. Benzmüller, C., Theiss, F., Paulson, L., and Fietzke, A. (2008). LEO-II - a cooperative automatic theorem prover for higher-order logic. In IJCAR, volume 5195 of LNCS, pages 162-170. Springer.
  7. Benzmller, C., Sorge, V., Jamnik, M., and Kerber, M. (2008). Combined reasoning by automated cooperation. J. Appl. Log., 6(3):318 - 342.
  8. Bonacina, M. (2000). A taxonomy of parallel strategies for deduction. Annals of Mathematics and Artificial Intelligence, 29(1-4):223-257.
  9. Gelernter, David and Bernstein, Arthur J./1982) Distributed Communication via Global Buffer. Proceedings of the First ACM SIGACT-SIGOPS, PODC 7882, pages 10- 18. ACM.
  10. Lusk, E. L., McCune, W., and Slaney, J. K. (1992). Roo: A parallel theorem prover. In CADE, volume 607 of LNCS, pages 731-734. Springer.
  11. Nisan, N., Roughgarden, T., Tardos, E., and Vazirani, V. V. (2007). Algorithmic Game Theory. Cambridge University Press, New York, NY, USA.
  12. Robinson, J. A. (1965). A machine-oriented logic based on the resolution principle. J. ACM, 12(1):23-41.
  13. Schumann, J. and Letz, R. (1990). Partheo: A highperformance parallel theorem prover. In CADE, volume 449 of LNCS, pages 40-56. Springer.
  14. Suttner, C. B. (1997). Sptheo - a parallel theorem prover. J. Autom. Reason., 18(2):253-258.
  15. Voronkov, A. (2014). AVATAR: the architecture for firstorder theorem provers. In CAV, volume 8559 in LNCS, pages 696-710. Springer.
  16. Weiss, G., editor (2013). Multiagent Systems. MIT Press.
  17. Wisniewski, M. (2014). Agent-based blackboard architecture for a higher-order theorem prover. Master's thesis, Freie Universität Berlin.
  18. Wisniewski, M., Steen, A., and Benzmüller, C. (2014). The Leo-III project. In Bolotov, A. and Kerber, M., editors, Joint Automated Reasoning Workshop and Deduktionstreffen, page 38.
  19. Wisniewski, M., Steen, A., and Benzmüller, C. (2015). Leopard - A generic platform for the implementation of higher-order reasoners. In Kerber, M., et al., editors, CICM, volume 9150 of LNCS, pages 325-330. Springer.
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Paper Citation


in Harvard Style

Wisniewski M. and Benzmüller C. (2016). Is It Reasonable to Employ Agents in Automated Theorem Proving? . In Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-758-172-4, pages 281-286. DOI: 10.5220/0005824702810286


in Bibtex Style

@conference{icaart16,
author={Max Wisniewski and Christoph Benzmüller},
title={Is It Reasonable to Employ Agents in Automated Theorem Proving?},
booktitle={Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2016},
pages={281-286},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005824702810286},
isbn={978-989-758-172-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - Is It Reasonable to Employ Agents in Automated Theorem Proving?
SN - 978-989-758-172-4
AU - Wisniewski M.
AU - Benzmüller C.
PY - 2016
SP - 281
EP - 286
DO - 10.5220/0005824702810286