Abstract
leanCoP is a very compact theorem prover for classical first-order logic, based on the connection (tableau) calculus and implemented in Prolog. leanCoP 2.0 enhances leanCoP 1.0 by adding regularity, lemmata, and a technique for restricting backtracking. It also provides a definitional translation into clausal form and integrates “Prolog technology” into a lean theorem prover. ileanCoP is a compact theorem prover for intuitionistic first-order logic and based on the clausal connection calculus for intuitionistic logic. leanCoP 2.0 extends the classical prover leanCoP 2.0 by adding prefixes and a prefix unification algorithm. We present details of both implementations and evaluate their performance.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Astrachan, O., Loveland, D.: METEORs: High Performance Theorem Provers Using Model Elimination. In: Bledsoe, W.W., Boyer, S. (eds.) Automated Reasoning: Essays in Honor of Woody Bledsoe, pp. 31–60. Kluwer, Amsterdam (1991)
Beckert, B., Posegga, J.: lean TA P: Lean Tableau-Based Theorem Proving. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 793–797. Springer, Heidelberg (1994)
Bibel, W.: Matings in Matrices. Commun. ACM 26, 844–852 (1983)
Bibel, W.: Automated Theorem Proving. Vieweg, Wiesbaden (1987)
Bibel, W., Brüning, S., Egly, U., Rath, T.: KoMeT. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 783–787. Springer, Heidelberg (1994)
Kreitz, C., Otten, J.: Connection-based Theorem Proving in Classical and Non-classical Logics. Journal of Universal Computer Science 5, 88–112 (1999)
Letz, R., Schumann, J., Bayerl, S., Bibel, W.: SETHEO: A High-Performance Theorem Prover. Journal of Automated Reasoning 8, 183–212 (1992)
Letz, R., Mayr, K., Goller, C.: Controlled Integration of the Cut Rule into Connection Tableaux Calculi. Journal of Automated Reasoning 13, 297–337 (1994)
Letz, R., Stenz, G.: Model Elimination and Connection Tableau Procedures. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 2015–2114. Elsevier, Amsterdam (2001)
Loveland, D.: Mechanical Theorem-Proving by Model Elimination. Journal of the ACM 15, 236–251 (1968)
McCune, W.: Otter 3.0 Reference Manual and Guide. Technical report ANL-94/6, Argonne National Laboratory (1994)
McCune, W.: Release of Prover9. In: Mile High Conference on Quasigroups, Loops and Nonassociative Systems, Technical report, Denver (2005)
Otten, J.: ileanT AP: An Intuitionistic Theorem Prover. In: Galmiche, D. (ed.) TABLEAUX 1997. LNCS, vol. 1227, pp. 307–312. Springer, Heidelberg (1997)
Otten, J.: Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 245–261. Springer, Heidelberg (2005)
Otten, J.: Restricting Backtracking in Connection Calculi. Technical report, Institut für Informatik, University of Potsdam (2008)
Otten, J., Bibel, W.: leanCoP: Lean Connection-based Theorem Proving. Journal of Symbolic Computation 36, 139–161 (2003)
Otten, J., Kreitz, C.: T-String-Unification: Unifying Prefixes in Non-classical Proof Methods. In: Miglioli, P., Moscato, U., Ornaghi, M., Mundici, D. (eds.) TABLEAUX 1996. LNCS, vol. 1071, pp. 244–260. Springer, Heidelberg (1996)
Raths, T., Otten, J.: randoCoP: Randomizing the Proof Search Order in the Connection Calculus. Technical report, Institut für Informatik, University of Potsdam (2008)
Raths, T., Otten, J., Kreitz, C.: The ILTP Problem Library for Intuitionistic Logic. Journal of Automated Reasoning 38, 261–271 (2007)
Sahlin, D., Franzen, T., Haridi, S.: An Intuitionistic Predicate Logic Theorem Prover. Journal of Logic and Computation 2, 619–656 (1992)
Schmitt, S., Lorigo, L., Kreitz, C., Nogin, A.: JProver: Integrating Connection-based Theorem Proving into Interactive Proof Assistants. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 421–426. Springer, Heidelberg (2001)
Stickel, M.: A Prolog Technology Theorem Prover: Implementation by an Extended Prolog Compiler. Journal of Automated Reasoning 4, 353–380 (1988)
Sutcliffe, G.: The CADE-21 Automated Theorem Proving System Competition. AI Communications 21, 71–81 (2008)
Sutcliffe, G., Suttner, C.: The TPTP Problem Library. Journal of Automated Reasoning 21, 177–203 (1998)
Urban, J.: MPTP 0.2: Design, Implementation, and Initial Experiments. Journal of Automated Reasoning 37, 21–43 (2006)
Tammet, T.: A Resolution Theorem Prover for Intuitionistic Logic. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 2–16. Springer, Heidelberg (1996)
Waaler, A.: Connections in Nonclassical Logics. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 1487–1578. Elsevier, Amsterdam (2001)
Wallen, L.: Automated Deduction in Nonclassical Logics. MIT Press, Cambridge (1990)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Otten, J. (2008). leanCoP 2.0 and ileanCoP 1.2: High Performance Lean Theorem Proving in Classical and Intuitionistic Logic (System Descriptions). In: Armando, A., Baumgartner, P., Dowek, G. (eds) Automated Reasoning. IJCAR 2008. Lecture Notes in Computer Science(), vol 5195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71070-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-71070-7_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71069-1
Online ISBN: 978-3-540-71070-7
eBook Packages: Computer ScienceComputer Science (R0)