Abstract
We propose a variant of ordered resolution with semantic restrictions based on interpretations which are identified by the given atom ordering and selection function. Techniques for effectively approximating validity (satisfiability) in these interpretations are presented. They are related to methods of soft typing for programming languages. The framework is shown to be strictly more general than certain previously introduced approaches. Implementation of some of our techniques in the Spass prover has lead to encouraging experimental results.
This work was supported by the German science foundation program Deduktion.
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
Bachmair, L. and Ganzinger, H. [1991], Perfect model semantics for logic programs with equality, in ‘Proc. International Conference on Logic Programming '91', MIT Press, pp. 645–659.
Bachmair, L. and Ganzinger, H. [1994], ‘Rewrite-based equational theorem proving with selection and simplification', Journal of Logic and Computation 4(3), 217–247. Revised version of Max-Planck-Institut für Informatik technical report, MPI-I-91-208, 1991.
Comon, H. [1995], Sequentiality, second order monadic logic and tree automata, in ‘Proceedings 10th IEEE Symposium on Logic in Computer Science, LICS'95', IEEE Computer Society Press, pp. 508–517.
Frühwirth, T., Shapiro, E., Vardi, M. Y. and Yardeni, E. [1991], Logic programs as types for logic programs, in A. R. Meyer, ed., ‘Proceedings of the 6th Annual IEEE Symposium on Logic in Computer Science, LICS'91', IEEE Computer Society Press, pp. 300–309.
Jacquemard, F. [1996], Decidable approximations of term rewriting systems, in H. Ganzinger, ed., ‘Rewriting Techniques and Applications, 7th International Conference, RTA-96', Vol. 1103 of LNCS, Springer, pp. 362–376.
Manthey, R. and Bry, F. [1988], Satchmo: A theorem prover implemented in prolog, in E. Lusk and R. Overbeek, eds, ‘9th International Conference on Automated Deduction, CADE-9', Vol. 310 of LNCS, Springer, pp. 415–434.
Nieuwenhuis, R. [1996], Basic paramodulation and decidable theories (extended abstract), in ‘Proceedings 11th IEEE Symposium on Logic in Computer Science, LICS'96', IEEE Computer Society Press, pp. 473–482.
Plaisted, D. A. [1994], Ordered semantic hyper-linking, Technical report, Max-Planck-Institut für Informatik, Saarbrücken.
Schmidt, R. A. [1997], Resolution is a decision procedure for many prepositional modal logics, Technical Report MPI-I-97-2-002, Max-Planck-Institut für Informatik, Saarbrücken, Germany. The extended abstract version is to appear in Kracht, M., de Rijke, M., Wansing, H. and Zakharyaschev, M. (eds) (1997), Advances in Modal Logic '96, CSLI Publications, Stanford.
Slagle, J. R. [1967], ‘Automatic theorem-proving with renamable and semantic resolution', Journal of the ACM 14, 687–697.
Weidenbach, C. [1996], Computational Aspects of a First-Order Logic with Sorts, Dissertation, Technische Fakultät der Universität des Saarlandes, Saarbrücken, Germany.
Weidenbach, C., Gaede, B. and Rock, G. [1996], SPASS & FLOTTER, Version 0.42, in M. McRobbie and J. Slaney, eds, ‘13th International Conference on Automated Deduction, CADE-13', Vol. 1104 of LNAI, Springer, pp. 141–145.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ganzinger, H., Meyer, C., Weidenbach, C. (1997). Soft typing for ordered resolution. In: McCune, W. (eds) Automated Deduction—CADE-14. CADE 1997. Lecture Notes in Computer Science, vol 1249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63104-6_32
Download citation
DOI: https://doi.org/10.1007/3-540-63104-6_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63104-0
Online ISBN: 978-3-540-69140-2
eBook Packages: Springer Book Archive