{"type":"ScholarlyArticle","title":"Negative Hyper-Resolution for Proving Statements Containing Transitive Relations","authors":[{"name":"Tamás Gergely","slug":"tamas-gergely","given":"Tamás","family":"Gergely","affiliation":""},{"name":"Konstantin Vershinin","slug":"konstantin-vershinin","given":"Konstantin","family":"Vershinin","affiliation":""}],"abstract":"A modified version of PHR-- resolution comprising negative hyper-resolution and paramodulation is introduced to reduce the search of statements that contain transitive relations. Let R be a symbol of transitive relation and let a nucleus contain the literal tRp, and let a factor of an electron be of the form C V r t 1 Rt 2 .Moreover let us suppose that tU = t u, where U is a simultaneous most general Onifier for the corresponding clash. Then the resolvent of this clash contains the subclause (C V pRt 2 )U. Th~s rule of deduction is said to oe TPHR - rule. It is shown that TPHR-- resolution is complete. More precisely, it is shown that the empty clause o can be deduced from a set G of clauses which contains the axiom of transitivity TrR for the relation R by using PHR-- resolution iff o can be deduced from the set G- {TrR} by using TPHR-- resolution. . The efficiency of the use of TPHR-rule is illustrated by examples.","doi":null,"url":"https://ijcai.org/proceedings/1983/210","pdf":"https://ijcai.org/proceedings/1983/0210.pdf","markdown":"https://ijcai.org/proceedings/1983/210.md","bibtex":"https://ijcai.org/proceedings/1983/bibtex/210","volume":{"slug":"1983","title":"Proceedings of the Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1983","url":"https://ijcai.org/proceedings/1983/","year":1983,"location":"Karlsruhe, West Germany","dates":"","editors":"Alan Bundy","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Theorem Proving","track":"Theorem Proving","number":210,"pages":{"first":877,"last":880},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}