{"type":"ScholarlyArticle","title":"An Equational Approach to Theorem Proving in First-Order Predicate Calculus","authors":[{"name":"Deepak Kapur","slug":"deepak-kapur","given":"Deepak","family":"Kapur","affiliation":"Computer Science Branch Corporate Research and Development General Electric Company Schenectady , New York"},{"name":"Paliath Narendran","slug":"paliath-narendran","given":"Paliath","family":"Narendran","affiliation":"Computer Science Branch Corporate Research and Development General Electric Company Schenectady , New York"}],"abstract":"A new approach for proving theorems in first-order predicate calculus is developed based on term rewriting and polynomial simplification methods . A formula is translated into an equivalent set of formulae expressed in terms of 'true', 'false ', 'exclusive-or', and 'and' by analyzing the semantics of its top-level operator. In this representation, formulae are polynomials over atomic formulae with 'and' as multiplication and 'exclusive-or' as addition, and they can be manipulated just like polynomials using familiar rules of multiplication and addition. Polynomials representing a formula are converted into rewrite rules which are used to simplify polynomials. New rules are generated by overlapping polynomials using a critical-pair completion procedure closely related to the Knuth- Bendix procedure. This process is repeated until a contradiction is reached or it is no Ionger possible to generate new rules. It is shown that resolution is subsumed by this method .","doi":null,"url":"https://ijcai.org/proceedings/1985/234","pdf":"https://ijcai.org/proceedings/1985/0234.pdf","markdown":"https://ijcai.org/proceedings/1985/234.md","bibtex":"https://ijcai.org/proceedings/1985/bibtex/234","volume":{"slug":"1985","title":"Proceedings of the Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1985","url":"https://ijcai.org/proceedings/1985/","year":1985,"location":"Los Angeles, California, USA","dates":"","editors":"Aravind Joshi","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Theorem Proving","track":"Theorem Proving","number":234,"pages":{"first":1146,"last":1152},"keywords":[],"videos":[],"references":[{"position":1,"raw":"Bledsoe, W. 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