{"type":"ScholarlyArticle","title":"Formal Grammars as Models of Logic Derivations","authors":[{"name":"Sharon Sickel","slug":"sharon-sickel","given":"Sharon","family":"Sickel","affiliation":""}],"abstract":"Context-free attribute grammars are proposed as derivational models for proofs in the predicate calculus. The new representation is developed and its correspondence to resolution-based clause interconnectivity graphs is established. The new representation may be used to transform a predicate calculus characterization of a problem into a regular algebra characterization of the solutions. The new representation can be used to simplify the search for proofs. It allows us to express and derive predicate calculus proofs as a constraining function that serves as a filter to the set of candidate proofs that ignore the arguments to predicates. The effect of this is to separate the underlying propositional structure from the re- . strictions imposed by the required unifications. While previous theorem proving methods have been able to enumerate all proofs of a theorem, the method reported here is unique in being able to characterize all proofs of some theorems, representing even an infinite set of proofs with a finite formula. This work has implications for proof theory as well as providing a useful tool in the analysis of programs specified in logic.","doi":null,"url":"https://ijcai.org/proceedings/1977/125","pdf":"https://ijcai.org/proceedings/1977/0125.pdf","markdown":"https://ijcai.org/proceedings/1977/125.md","bibtex":"https://ijcai.org/proceedings/1977/bibtex/125","volume":{"slug":"1977","title":"Proceedings of the Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1977","url":"https://ijcai.org/proceedings/1977/","year":1977,"location":"Cambridge, MA, USA","dates":"","editors":"Raj Reddy","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Theorem Proving","track":"Theorem Proving","number":125,"pages":{"first":544,"last":550},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}