{"type":"ScholarlyArticle","title":"An Extension of Unification to Substitution with an Application to Automatic Theorem Proving","authors":[{"name":"J. van Vaalen","slug":"j-van-vaalen","given":"J.","family":"van Vaalen","affiliation":""}],"abstract":"The notion of unifiability is extended to substitutions. Theorems concerning this notion are derived together with an algorithm for computing the most general unifier of a set of substitutions.Especially fruitful! is the application in the case of the and-or tree approach to theorem proving where the subgoals are not independent but contain the same variables. Here the ultimate solution is shown to be the most general instance of the solutions to the individual subproblems. Another application concerns connection graphs where the arcs are substitutions and new arcs can be generated from old arcs.","doi":null,"url":"https://ijcai.org/proceedings/1975/13","pdf":"https://ijcai.org/proceedings/1975/0013.pdf","markdown":"https://ijcai.org/proceedings/1975/13.md","bibtex":"https://ijcai.org/proceedings/1975/bibtex/13","volume":{"slug":"1975","title":"Proceedings of the Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1975","url":"https://ijcai.org/proceedings/1975/","year":1975,"location":"Tbilisi, Georgia, USSR","dates":"","editors":"Patrick Winston and Carl Hewitt","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Mathematical and Theoretical Aspects of A.I","track":"Mathematical and Theoretical Aspects of A.I","number":13,"pages":{"first":77,"last":81},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}