Efficient implementation of non-standard connectives and quantifiers in deductive reasoning systems

A rule use information (RUI) structure has been proposed to implement nonstandard connectives and quantifiers that generalize conjunction, disjunction, implication, universal quantifier, and existential quantifier. The current implementation of the RUI structure in the SNePS Inference Package (SNIP) maintains 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. The problem of efficient RUI handling for deduction rules with non-standard connectives and quantifiers is addressed. Two kinds of algorithms are proposed, and methods of distributing RUIs over several 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.<
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