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Rewrite techniques for transitive relations

Bachmair, Leo and Ganzinger, Harald

November 1993, 19 pages.

Status: available - back from printing

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.
Short version in Proc.~LICS'94, pp.\ 384--393, 1994

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  AUTHOR = {Bachmair, Leo and Ganzinger, Harald},
  TITLE = {Rewrite techniques for transitive relations},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-93-249},
  MONTH = {November},
  YEAR = {1993},
  ISSN = {0946-011X},
  NOTE = {Short version in Proc.~LICS'94, pp.\ 384--393, 1994},