Advanced indexing operations on substitution trees
Indexing techniques support the retrieval and maintenance of large sets of terms. There is also an indexing method called substitution tree indexing that efficiently handles sets of substitutions. We present three advanced indexing operations for substitution trees: The multi-merge for the simultaneous unification of sets of substitutions, the subsumption operation on two sets of substitutions, and the selection of ‘lightest’ substitutions of a set of substitutions. The indexing operations can be combined to obtain powerful reasoning tools for theorem provers.
Unable to display preview. Download preview PDF.
- 2.C.L. Chang and R.C.T. Lee. Symbolic Logic and Mechanical Theorem Proving. Computer Science and Applied Mathematics. Academic Press, New York, New York, 1973.Google Scholar
- 3.P. Graf. Substitution tree indexing. In 6th International Conference on Rewriting Techniques and Applications RTA-95, pages 117–131. Springer LNCS 914, 1995.Google Scholar
- 4.P. Graf. Term Indexing. Springer LNAI 1053, 1996.Google Scholar
- 7.C. Meyer. Parallel Unit Resulting Resolution. Diploma thesis, Universität des Saarlandes, Saarbrücken, Germany, 1996. http://www.mpi-sb.mpg.de/papers/masters_theses/meyer.ps.gz.Google Scholar
- 8.H.J. Ohlbach. Abstraction tree indexing for terms. In Proceedings of the 9th European Conference on Artificial Intelligence, pages 479–484. Pitman Publishing, London, August 1990.Google Scholar
- 9.J. A. Robinson. Automated deduction with hyper-resolution. International Journal of Comp. Mathematics, 1:227–234, 1965.Google Scholar