Eecient Implementation of Non-standard Connectives and Quantiiers in Deductive Reasoning Systems

A rule use information RUI structure has been proposed to implement non standard connectives and quanti ers that generalize conjunction disjunction implication universal quanti er and existential quan ti er The current implementation of the RUI struc ture in the SNePS Inference Package SNIP main tains a single RUI set for each rule which causes a combinatorial number of substitution compatibility checks between RUIs as the number of antecedents in a rule and their instances increase In this paper the problem of e cient RUI handling for deduction rules with non standard connectives and quanti ers is addressed Two kinds of algorithms are proposed and methods of distributing RUIs over sev eral sets are discussed Complexity analyses and test results show that these schemes of RUI set distribution keep the complexity of RUI set handling to polynomial in terms of the number of RUIs and the number of substitution compatibility tests