Abstract
This talk discusses some of the challenges of building a usable theorem prover. These include the chasm between theory and code, conflicting requirements, feature interaction, and competitive performance. The talk draws on the speaker’s experiences with devising extensions of resolution and building theorem provers that have been used as embedded reasoners in various systems.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Amir, E., Maynard-Zhang, P.: Logic-based subsumption architecture. Artificial Intelligence 153(1-2), 167–237 (2004)
Baader, F., Calvanese, D., McGuiness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge (2003)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Brachman, R.J., Levesque, H.J.: Knowledge Representation and Reasoning. Morgan Kaufmann, San Francisco (2004)
Chang, C.-L., Lee, R.C.-T.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, London (1973)
Dantsin, E., Voronkov, A.: A nondeterministic polynomial-time unification algorithm for bags, sets and trees. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 180–196. Springer, Heidelberg (1999)
Dixon, J.K.: Z-resolution: Theorem-proving with compiled axioms. J. ACM 20(1), 127–147 (1973)
Fages, F.: Associative-commutative unification. J. Symbolic Computation 3(3), 257–275 (1987)
Frisch, A.M.: The substitutional framework for sorted deduction: Fundamental results on hybrid reasoning. Artificial Intelligence 49(1-3), 161–198 (1991)
Graf, P.: Term Indexing. LNCS (LNAI), vol. 1053. Springer, Heidelberg (1996)
Green, C.: Theorem-proving by resolution as a basis for question-answering systems. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence 4, pp. 183–205. Edinburgh University Press (1969)
Korf, R.E.: Iterative-deepening-A*: An optimal admissible tree search. In: IJCAI, pp. 1034–1036 (1985)
Korovin, K., Voronkov, A.: An AC-compatible Knuth-Bendix order. In: Baader, F. (ed.) CADE 2003. LNCS, vol. 2741, pp. 47–59. Springer, Heidelberg (2003)
Löchner, B.: Things to know when implementing LPO. International Journal on Artificial Intelligence Tools 15(1), 53–80 (2006)
Loveland, D.W.: A simplified format for the model elimination theorem-proving procedure. J. ACM 16(3), 349–363 (1969)
Loveland, D.W.: Automated Theorem Proving: A Logical Basis. North-Holland, Amsterdam (1978)
Lowry, M., Philpot, A., Pressburger, T., Underwood, I., Waldinger, R., Stickel, M.: Amphion: Automatic programming for the NAIF toolkit. NASA Science Information Systems Newsletter 31, 22–25 (1994)
Manna, Z., Waldinger, R.J.: A deductive approach to program synthesis. ACM Trans. Programming Languages and Systems 2(1), 90–121 (1980)
McCune, W.: Solution of the robbins problem. J. Automated Reasoning 19(3), 263–276 (1997)
McCune, W.: Otter 3.3 reference manual. Technical Memorandum 263, Mathematics and Computer Science Divison, Argonne National Laboratory (August 2003)
McCune, W., Wos, L.: Experiments in automated deduction with condensed detachment. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 209–223. Springer, Heidelberg (1992)
Newell, A., Shaw, J.C., Simon, H.A.: Empirical explorations with the logic theory machine: a case study in heuristics. In: Feigenbaum, E.A., Feldman, J. (eds.) Computers and Thought, pp. 109–133. McGraw-Hill, New York (1963)
Paskevich, A.: Connection tableaux with lazy paramodulation. J. Automated Reasoning 40(2-3), 179–194 (2008)
Peterson, G.E., Stickel, M.E.: Complete sets of reductions for some equational theories. J. ACM 28(2), 233–264 (1981)
Rubio, A.: A fully syntactic AC-RPO. Inf. Comput. 178(2), 515–533 (2002)
Sekar, R., Ramakrishnan, I.V., Voronkov, A.: Term indexing. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 1853–1964. MIT Press, Cambridge (2001)
Shrager, J., Waldinger, R., Stickel, M., Massar, J.P.: Deductive biocomputing. PLoS ONE 2(4), e339 (2007)
Slagle, J.R.: Experiments with a deductive question-answering program. Commun. ACM 8(12), 792–798 (1965)
Snyder, W., Lynch, C.: Goal directed strategies for paramodulation. In: Book, R.V. (ed.) RTA 1991. LNCS, vol. 488, pp. 150–161. Springer, Heidelberg (1991)
Stickel, M.E.: A unification algorithm for associative-commutative functions. J. ACM 28(3), 423–434 (1981)
Stickel, M.E.: Automated deduction by theory resolution. J. Automated Reasoning 1(4), 333–355 (1985)
Stickel, M.E.: A Prolog technology theorem prover: Implementation by an extended Prolog compiler. J. Automated Reasoning 4(4), 353–380 (1988)
Stickel, M.E.: A Prolog technology theorem prover: A new exposition and implementation in Prolog. Theoretical Computer Science 104(1), 109–128 (1992)
Stickel, M.E., Tyson, M.: An analysis of consecutively bounded depth-first search with applications in automated deduction. In: IJCAI, pp. 1073–1075 (1985)
Stickel, M.E., Waldinger, R.J., Chaudhri, V.K.: A guide to Snark. Technical report, Artificial Intelligence Center, SRI International (May 2000), http://www.ai.sri.com/snark/tutorial/tutorial.html
Stickel, M.E., Waldinger, R.J., Lowry, M.R., Pressburger, T., Underwood, I.: Deductive composition of astronomical software from subroutine libraries. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 341–355. Springer, Heidelberg (1994)
Tammet, T.: Chain resolution for the semantic web. In: Basin, D.A., Rusinowitch, M. (eds.) IJCAR 2004. LNCS, vol. 3097, pp. 307–320. Springer, Heidelberg (2004)
Waldinger, R., Appelt, D.E., Dungan, J.L., Fry, J., Hobbs, J., Israel, D.J., Jarvis, P., Martin, D., Riehemann, S., Stickel, M.E., Tyson, M.: Deductive question answering from multiple resources. In: Maybury, M.T. (ed.) New Directions in Question Answering, pp. 253–262. AAAI Press, Menlo Park (2004)
Waldinger, R.J.: Whatever happened to deductive question answering? In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS, vol. 4790, pp. 15–16. Springer, Heidelberg (2007)
Walther, C.: A Many-Sorted Calculus Based on Resolution and Paramodulation. Pitman, London (1987)
Wos, L.: Automated Reasoning: 33 Basic Research Problems. Prentice-Hall, Englewood Cliffs (1988)
Wos, L.: A milestone reached and a secret revealed. J. Automated Reasoning 27(2), 89–95 (2001)
Wos, L.: From the AAR president. Association for Automated Reasoning Newsletter 83 (April 2009)
Wos, L., Overbeek, R.A., Lusk, E.L.: Subsumption, a sometimes undervalued procedure. In: Lassez, J.-L., Plotkin, G. (eds.) Computational Logic - Essays in Honor of Alan Robinson, pp. 3–40 (1991)
Wos, L., Pieper, G.W.: Automated Reasoning and the Discovery of Missing and Elegant Proofs. Rinton Press, Paramus (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stickel, M.E. (2009). Building Theorem Provers. In: Schmidt, R.A. (eds) Automated Deduction – CADE-22. CADE 2009. Lecture Notes in Computer Science(), vol 5663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02959-2_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-02959-2_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02958-5
Online ISBN: 978-3-642-02959-2
eBook Packages: Computer ScienceComputer Science (R0)