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Paradox (theorem prover)

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Paradox
Developer(s)
  • Koen Lindström Claessen
  • Niklas Sörensson
Written inHaskell
TypeAutomated theorem proving
LicenseGNU General Public License

Paradox is a finite-domain model finder for pure first-order logic (FOL) with equality developed by Koen Lindström Claessen and Niklas Sörensson at the Chalmers University of Technology.[1][2] It can a participate as part of an automated theorem proving system.[2] The software is primarily written in the Haskell programming language.[3] It is released under the terms of the GNU General Public License and is free.[4]

Features

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The Paradox developers described the software as a Mace-style method after the McCune's tool of that name.[5][6] The Paradox introduced new techniques which help to reduce the computational complexity of the model search problem:[5]

  • term definitions, new variable reduction technique,
  • incremental satisfiability checker which works with small domains first, then gradually increases the size of the domain, reusing the information it obtained from previous failed searches,
  • static symmetry reduction which adds extra constraints,
  • sort inference which works with unsorted problems.

Paradox was developed up to version 4, the final version being effective in model finding for Web Ontology Language OWL2.[7]

Competition

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Paradox was a division winner in the annual CADE ATP System Competition, an annual contest for automated theorem proving, in the years 2003 to 2012.[8]

References

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  1. ^ "Paradox". Chalmers University of Technology. Archived from the original on 8 January 2007. Retrieved 26 May 2007.
  2. ^ a b Pudlák, Petr (17 July 2007). "Semantic Selection of Premisses for Automated Theorem Proving" (PDF). In Urban, J.; Sutcliffe, G.; Schulz, S. (eds.). Proceedings of the CADE-21 Workshop on Empirically Successful Automated Reasoning in Large Theories. The 21st International Conference on Automated Deduction. CEUR Workshop Proceedings. Vol. 257. Bremen. pp. 27–44. ISSN 1613-0073. S2CID 16318678. Archived from the original (PDF) on 7 November 2018. Retrieved 7 November 2011.
  3. ^ "Entrants' System Descriptions". University of Miami. Paradox 3.0. Archived from the original on 7 November 2018. Retrieved 7 November 2018.
  4. ^ "Paradox". Chalmers University of Technology. Archived from the original on 15 January 2007. Retrieved 30 April 2020.
  5. ^ a b Claessen, Koen; Sörensson, Niklas. "New Techniques that Improve MACE-style Finite Model Finding" (PDF). S2CID 15694927. Archived from the original (PDF) on 11 November 2018. Retrieved 11 November 2018.
  6. ^ "Automated Theorem Proving" (PDF). Australian National University College of Engineering & Computer Science. pp. 73–74. Archived (PDF) from the original on 11 November 2018. Retrieved 11 November 2018.
  7. ^ Schneider, Michael; Sutcliffe, Geoff (2011). "Reasoning in the OWL 2 Full Ontology Language using First-Order Automated Theorem Proving". arXiv:1108.0155 [cs.AI].
  8. ^ "The CADE ATP System Competition - The World Championship for Automated Theorem Proving". Previous CASCs' Division Winners. Archived from the original on 1 September 2018. Retrieved 7 November 2018.
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