## Paper: Rewrite techniques for transitive relations (at LICS 1994)

**Leo Bachmair Harald Ganzinger**

### Abstract

We propose inference systems for dealing with transitive relations in the context of resolution-type theorem proving. These inference mechanisms are based on standard techniques from term rewriting and represent a refinement of chaining methods. We establish their refutational completeness and also prove their compatibility with the usual simplification techniques used in rewrite-based theorem provers. A key to the practicality of chaining techniques is the extent to which so-called variable chainings can be restricted. We demonstrate that rewrite techniques considerably restrict variable chaining, though we also show that they cannot be completely avoided for transitive relations in general. If the given relation satisfies additional properties, such as symmetry, further restrictions are possible. In particular, we discuss (partial) equivalence relations and congruence relations

### BibTeX

@InProceedings{BachmairGanzinger-Rewritetechniquesfo, author = {Leo Bachmair and Harald Ganzinger}, title = {Rewrite techniques for transitive relations}, booktitle = {Proceedings of the Ninth Annual IEEE Symposium on Logic in Computer Science (LICS 1994)}, year = {1994}, month = {July}, pages = {384--393}, location = {Paris, France}, publisher = {IEEE Computer Society Press} }