Abstract
We prove the completeness of the regular strategy of derivations for superposition-based calculi. The regular strategy was pioneered by Kanger in [Kan63], who proposed that all equality inferences take place before all other steps in the proof. We show that the strategy is complete with the elimination of tautologies. The implication of our result is the completeness of non-standard selection functions by which in non-relational clauses only equality literals (and all of them) are selected.
This is a preview of subscription content, log in via an institution to check access.
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
Aleksić, V., Degtyarev, A.: On arbitrary selection strategies for superposition. Proceedings of FTP, Technical Report of the University of Koblenz (September 2005)
Bachmair, L., Ganzinger, H., Lynch, C., Snyder, W.: Basic paramodulation and superposition. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 462–476. Springer, Heidelberg (1992)
Bachmair, L., Ganzinger, H.: Strict basic superposition and chaining. Research report MPI-I-97-2-011, Max-Planck-Institut für Informatic, Saarbrücken
Bofill, L., Godoy, G.: On the completeness of arbitrary selection strategies for paramoduletion. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 951–962. Springer, Heidelberg (2001)
Bofill, L., Rubio, A.: Well-foundedness is sufficient for completeness of ordered paramodulation. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 456–470. Springer, Heidelberg (2002)
Degtyarev, A., Voronkov, A.: Equality reasoning in sequent-based calculi. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 613–706. Elsevier Science Publishers B.V, Amsterdam (2001)
Degtyarev, A., Voronkov, A.: Handling equality in logic programs via basic folding. In: Herre, H., Dyckhoff, R., Schroeder-Heister, P. (eds.) ELP 1996. LNCS, vol. 1050, pp. 119–136. Springer, Heidelberg (1996)
Kanger, S.: A simplified proof method for elementary logic. In: Siekmann, J., Wrightson, G. (eds.) Automation of Reasoning. Classical Papers on Computational Logic, vol. 1, pp. 364–371. Springer, Heidelberg (1963) (Originally appeared in 1963)
Moser, M., Lynch, C., Steinbach, J.: Model Elimination with Basic Ordered Paramodulation.
Lynch, C.: Oriented Equational Logic is Complete. Journal of Symbolic Computations, 23(1):23–45 (1997). Technical Report AR-95-11, TU München (1995)
Nieuwenhuis, R., Rubio, A.: Basic superposition is complete. In: Krieg-Brückner, B. (ed.) ESOP 1992. LNCS, vol. 582, pp. 371–389. Springer, Heidelberg (1992)
Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 3–73. Elsevier Science Publishers B.V, Amsterdam (1999)
de Nivelle, H.: Ordering refinements of resolution. Dissertation, Technische Universiteit Delft, Delft (1996)
Robinson, G., Wos, L.: Completeness of paramodulation. Journal of Symbolic Logic 34(1), 159–160 (1969)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aleksić, V., Degtyarev, A. (2005). Regular Derivations in Basic Superposition-Based Calculi. In: Sutcliffe, G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11591191_21
Download citation
DOI: https://doi.org/10.1007/11591191_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30553-8
Online ISBN: 978-3-540-31650-3
eBook Packages: Computer ScienceComputer Science (R0)