Abstract
The method of proving refutational completeness via semantic trees is extended to cope with some new proof search refinements of resolution. It is also shown that a broad class of refinements can be combined with various deletion rules and a strong restriction on factoring without loosing completeness.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baaz, M., Fermüller, C.G.: Resolution-based Theorem Proving for Many-valued Logics. J. Symbolic Computation 11 (1995) 353–391
Chang, C.-L., Lee, R.C.-T.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York and London, 1973
Eisinger, N., Ohlbach, H.-J., Präcklein, A.: Reduction Rules for Resolution-Based Systems. J. Artificial Intelligence 50 (1991) 141–181
Fermüller, C.G.: Resolution Variant Deciding Some Classes of Clause Sets. In: Computer Science Logic (CSL'90), Heidelberg, Germany, eds. E. Börger et al., Springer Verlag, LNCS 533 (1991) 128–144
Fermüller, C.G.: A Simple Resolution Based Decision Procedure for the Maslov Class. In: Developments in Theoretical Computer Science, Proceedings of the 7th IMYCS, Smolenice 1992, Gordon & Breach, 1994, 197–204
Fermüller, C.G., Leitsch, A., Tammet, T., Zamov, N.: Resolution Methods for the Decision Problem. Springer Verlag, LNAI 679 (1993)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theorie of NP-completenes. W.H. Freeman, San Francisco, 1979
Gottlob, G., Fermüller, C.G.: Removing Redundancy from a Clause. J. Artificial Intelligence 61 (1993) 263–289
Hsiang, J., Rusinowitch, M.: Proving Refutational Completeness of TheoremProving Strategies: The Transfinite Semantic Tree Method. J. Assoc. of Comp. Mach. 38 (1991) 559–587
Joyner, W.H.: Resolution Strategies as Decision Procedures. J. Assoc. of Comp. Mach. 23 (1976) 398–417
Kowalski R., Hayes, P.J.: Semantic Trees in Automated Theorem Proving. In: Machine Intelligence 4 (1969), eds. B. Meltzer and D. Michie, Edinburgh University Press, 87–101
Leitsch, A.: On Different Concepts of Resolution. Zeitschr. f. math. Logik und Grundlagen d. Math. 35 (1989) 71–77
Loveland, D.: Automated Theorem Proving — A Logical Basis. North Holland, Amsterdam, New York, Oxford, 1978
McCune W.: Otter 3.0 Users Guide. Argonne National Laboratory, Argonne (Ill.), 1990
Noll, H.: A Note on Resolution: How to Get Rid of Factoring Without Loosing Completeness. In: 5th Conference on Automated Deduction, Springer Verlag, LNCS 87 (1980) 250–263
Robinson, J.A.: A Machine Oriented Logic Based on the Resolution Principle. J. Assoc. of Comp. Mach. 12 (1965) 23–41
Robinson, J.A.: The Generalized Resolution Principle. In: Machine Intelligence 3 (1968), ed. D. Michie, Edinburgh University Press, 77–93
Slagle, J.R.: Automatic Theorem Proving with Renamable and Semantic Resolution. J. Assoc. of Comp. Mach. 14 (1967) 687–697
Weidenbach, C.: Minimal Resolution. Max-Planck-Institut für Informatik, Technical report MPI-I-94-227, Saarbrücken, 1994
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fermüller, C.G. (1996). Semantic trees revisited: Some new completeness results. In: McRobbie, M.A., Slaney, J.K. (eds) Automated Deduction — Cade-13. CADE 1996. Lecture Notes in Computer Science, vol 1104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61511-3_114
Download citation
DOI: https://doi.org/10.1007/3-540-61511-3_114
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61511-8
Online ISBN: 978-3-540-68687-3
eBook Packages: Springer Book Archive