Abstract
We consider proof systems for effectively propositional logic. First, we show that propositional resolution for effectively propositional logic may have exponentially longer refutations than resolution for this logic. This shows that methods based on ground instantiation may be weaker than non-ground methods. Second, we introduce a generalisation rule for effectively propositional logic and show that resolution for this logic may have exponentially longer proofs than resolution with generalisation. We also discuss some related questions, such as sort assignments for generalisation.
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References
Baumgartner, P., Tinelli, C.: The model evolution calculus. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 350–364. Springer, Heidelberg (2003)
Billon, J.-P.: The disconnection method. A confluent integration of unification in the analytic framework. In: TABLEAUX 2006: Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Terrasini, Italy. LNCS (LNAI), vol. 1071, pp. 110–126. Springer, Heidelberg (1996)
Claessen, K., Sörensson, N.: New techniques that improve MACE-style model finding. In: MODEL 2003: Proceedings of the Workshop on Model Computation (2003)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of the ACM 5, 394–397 (1962)
Fuchs, A.: Darwin: A theorem prover for the model evolution calculus. Master’s thesis, University of Koblenz-Landau (2004)
Ganzinger, H., Korovin, K.: New directions in instantiation-based theorem proving. In: LICS 2003: Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science, Ottawa, Canada, June 2003, vol. 2, p. 55. IEEE Computer Society, Los Alamitos (1884)
Hooker, J.N., Rago, G., Chandru, V., Shrivastava, A.: Partial instantiation methods for inference in first order logic. Journal of Automated Reasoning 28(3), 371–396 (2002)
Korovin, K.: Implementing an instantiation-based theorem prover for first-order logic. In: Benzmueller, C., Fischer, B., Sutcliffe, G. (eds.) IWIL 2006: Proceedings of the 6th International Workshop on the Implementation of Logics, held at the 13th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR 2006). CEUR Workshop Proceedings, Phnom Penh, Cambodia, vol. 212 (2006), http://www.cs.man.ac.uk/~korovink/iprover/
Lee, S.-J., Plaisted, D.A.: Eliminating duplication with the hyper-linking strategy. Journal of Automated Reasoning 9(1), 25–42 (1992)
Letz, R., Stenz, G.: DCTP: A disconnection calculus theorem prover. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 381–385. Springer, Heidelberg (2001)
Navarro Pérez, J.A., Voronkov, A.: Encodings of bounded LTL model checking in effectively propositional logic. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 346–361. Springer, Heidelberg (2007)
Pérez, J.A.N., Voronkov, A.: Planning with effectively propositional logic. In: Collection of Papers Dedicated to Harald Ganzinger’s Memory (to appear, 2007)
Pelletier, F.J., Sutcliffe, G., Suttner, C.B.: The development of CASC. AI Communications 15(2), 79–90 (2002)
Plaisted, D.A., Zhu, Y.: Ordered semantic hyper-linking. Journal of Automated Reasoning 25(3), 167–217 (2000)
Plaisted, D.A., Zhu, Y.: The Efficiency of Theorem Proving Strategies. Computational Intelligence. Vieweg, Wiesbaden, Germany (1997)
Riazanov, A., Voronkov, A.: The design and implementation of Vampire. AI Communications 15(2), 91–110 (2002)
Schulz, S.: A comparison of different techniques for grounding near-propositional CNF formulae. In: Haller, S., Simmons, G. (eds.) FLAIRS 2002: Proceedings of the Fifteenth International Florida Artificial Intelligence Research Society Conference, pp. 72–76. AAAI Press, Menlo Park (2002)
Sutcliffe, G.: The CADE-21 ATP system competition website (2007), http://www.cs.miami.edu/~tptp/CASC/21/
Sutcliffe, G., Suttner, C.B.: The TPTP problem library: CNF release v1.2.1. Journal of Automated Reasoning 21(2), 177–203 (1998)
Tammet, T., Kadarpik, V.: Combining an inference engine with database: A rule server. In: Schröder, M., Wagner, G. (eds.) RuleML 2003. LNCS, vol. 2876, pp. 136–149. Springer, Heidelberg (2003)
Voronkov, A.: Merging relational database technology with the constraint technology. In: Perspectives of System Informatics. Andrei Ershov Second International Memorial Conference (Preliminary Proceedings), Novosibirsk, Akademgorodok, Russia, June 1996, pp. 189–195 (1996)
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Navarro, J.A., Voronkov, A. (2008). Proof Systems for Effectively Propositional Logic. 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_36
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DOI: https://doi.org/10.1007/978-3-540-71070-7_36
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