Cleary, John G.2016-02-242016-02-241993-10Cleary, J.G. (1993). Proving the existence of solutions in logical arithmetic. (Working paper 93/5). Hamilton, New Zealand: University of Waikato, Department of Computer Science.1170-487Xhttps://hdl.handle.net/10289/9960Logical arithmetic is a logically correct technique for real arithmetic in Prolog which uses constraints over interval representations for its implementation. Four problems with the technique are considered: answers are conditional and uninformative; iterative computations may lead to unboundedly large constraint networks; it is difficult and ineffective to deal with negation; and computing extrema is often not effective. A solution to these problems is proposed in the form of "existential intervals" which record the existence of a solution to a set of constraints within an interval. It is shown how to operate on existential intervals and how they solve the four problems.application/pdfen© 1993 John G. Cleary.computer scienceWorking Paper