Solving problems by formula manipulation in logic and linear inequalities

✍ Scribed by Louis Hodes

• Publisher: Elsevier Science
• Year: 1972
• Tongue: English
• Weight: 650 KB
• Volume: 3
• Category: Article
• ISSN: 0004-3702
• DOI: 10.1016/0004-3702(72)90046-x

✦ Synopsis

Using formal logic, many iproblems from the general area of linear inequalities co~ be expressed in the elementary theory of addition on the real numbers (EAR). We describe a method for eliminatit~ quantiflers in EAR which has been programmed arm demonstrate its usefulness in solving some problems related to linear programming. In the area of mechanical mathematics this kind of approach has been neglected in favor of more generalized method r based on Herbrand expansion. However, in a restricted area, such as linear inequalities, the use of these ~pecialized methods can increaye e.O~cieney by several orders of maonitud~ over an axiomatic Herbrand approach, aJut make practical problems accessible.