|Author||Bachmair, Leo ♦ Ganzinger, Harald|
|Source||ACM Digital Library|
|Publisher||Association for Computing Machinery (ACM)|
|Subject Domain (in DDC)||Computer science, information & general works ♦ Data processing & computer science|
|Subject Keyword||Chaining calculi ♦ Equational logic ♦ Reduction orderings ♦ Rewrite systems ♦ Term rewriting ♦ Transitive relations|
|Abstract||We propose inference systems for binary relations that satisfy composition laws such as transitivity. Our inference mechanisms are based on standard techniques from term rewriting and represent a refinement of chaining methods as they are used in the context of resolution-type theorem proving. We establish the refutational completeness of these calculi and prove that our methods are compatible with the usual simplification techniques employed in refutational theorem provers, such as subsumption or tautology deletion. Various optimizations of the basic chaining calculus will be discussed for theories with equality and for total orderings. A key to the practicality of chaining methods is the extent to which so-called variable chaining can be avoided. We demonstrate that rewrite techniques considerably restrict variable chaining and that further restrictions are possible if the transitive relation under consideration satisfies additional properties, such as symmetry. But we also show that variable chaining cannot be completely avoided in general.|
|Age Range||18 to 22 years ♦ above 22 year|
|Education Level||UG and PG|
|Learning Resource Type||Article|
|Publisher Place||New York|
|Journal||Journal of the ACM (JACM)|
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