Unification and Matching in Hierarchical Combinations of Syntactic Theories
We investigate a hierarchical combination approach to the unification problem in non-disjoint unions of equational theories. In this approach, the idea is to extend a base theory with some additional axioms given by rewrite rules in such way that the unification algorithm known for the base theory can be reused without loss of completeness. Additional techniques are required to solve a combined problem by reducing it to a problem in the base theory. In this paper we show that the hierarchical combination approach applies successfully to some classes of syntactic theories, such as shallow theories since the required unification algorithms needed for the combination algorithm can always be obtained. We also consider the matching problem in syntactic extensions of a base theory. Due to the more restricted nature of the matching problem, we obtain several improvements over the unification problem.
KeywordsInference Rule Combination Method Equational Theory Match Problem Combination Algorithm
Unable to display preview. Download preview PDF.
- 3.Baader, F., Snyder, W.: Unification theory. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 445–532. Elsevier and MIT Press (2001)Google Scholar
- 8.Erbatur, S., Kapur, D., Marshall, A.M., Narendran, P., Ringeissen, C.: Hierarchical combination of matching algorithms. In: Twentyeighth International Workshop on Unification (UNIF 2014), Vienna, Austria (2014)Google Scholar
- 12.Kirchner, C., Klay, F.: Syntactic theories and unification. In: Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science Logic in Computer Science, LICS 1990, pp. 270–277, June1990Google Scholar
- 15.Nipkow, T.: Proof transformations for equational theories. In: Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science Logic in Computer Science, LICS 1990, pp. 278–288, June 1990Google Scholar
- 19.Snyder, W.: A Proof Theory for General Unification. Progress in Computer Science and Applied Logic, vol. 11. Birkhäuser (1991)Google Scholar