A Method of Simplifying Many-Valued Generalized Quantifiers Tableau Rules Based on Boolean Pruning

As one of effective automated reasoning methods, Tableau has been apply to many important fields. Tableau methods with generalized quantifiers are very difficulty for computer to implement. Because the number of the branches extended is very large, a Boolean pruning method was proposed in many-valued logic. Tableau rules with such quantifiers can been simplified by providing a link between signed formulas and upset/downset in Boolean set lattices. On the basis of the presented Boolean pruning method, authors research on simplifying Tableau reasoning method for generalized meet and join to build a set of reasoning methods with generalized quantifiers in first-order many-valued logic. Through the analyses of examples and compare its performance to former approach, the result shows the improved Tableau method can have a great enhancement of the inference efficiency.