Refutational proofs of geometry theorems via characteristic set computation

Abstract

A refutational approach to geometry theorem proving using Ritt-Wu's algorithm for computing a characteristic set is discussed. A geometry problem is specified as a quantifier-free formula consisting of a finite set of hypotheses implying a conclusion, where each hypothesis is either a geometry relation or a subsidiary condition ruling out degenerate cases, and the conclusion is another geometry relation. The conclusion is negated, and each of the hypotheses (including the subsidiary conditions) and the negated conclusion is converted to a polynomial equation. Characteristic set computation is used for checking the inconsistency of a finite set of polynomial equations over an algebraic closed field. The method is contrasted with a related refutational method that used Buchberger's Grobner basis algorithm for the inconsistency check.