{"type":"ScholarlyArticle","title":"Solving Problems by Formula Manipulation in Logic and Linear Inequalities","authors":[{"name":"Louis Hodes","slug":"louis-hodes","given":"Louis","family":"Hodes","affiliation":""}],"abstract":"Using formal logic, many problems from the g eneral area of linear inequalities can be exp ress ed in the elementary theory of addition on the real numbers (EAR) . We describe a method for e l i mi nat i ng quantifiers i n EAR which has been pr ogr ammed and demonstrate its usefulness in s ol ving some problems related to linear prog ra mmi ng. I n the area of mechanical mathematics this kind of app r oach has been neglected in favor of more g eneralized methods based on Herbrand expa n sio n. However, in a restricted area, such as l i nea r inequalities, the use of these specialized me t hod s can increase efficiency by several orders of ma g nitude ov er an axiomatic Herbrand approach, and ma ke p ra c tical problems accessible.","doi":null,"url":"https://ijcai.org/proceedings/1971/58","pdf":"https://ijcai.org/proceedings/1971/0058.pdf","markdown":"https://ijcai.org/proceedings/1971/58.md","bibtex":"https://ijcai.org/proceedings/1971/bibtex/58","volume":{"slug":"1971","title":"Proceedings of the Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1971","url":"https://ijcai.org/proceedings/1971/","year":1971,"location":"London, UK","dates":"","editors":"D.C. Cooper","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":58,"pages":{"first":553,"last":558},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}