Higher-Order Quantification and Proof Search

Logical equivalence between logic programs that are firstorder logic formulas holds between few logic programs, partly because first-order logic does not allow auxiliary programs and data structures to be hidden. As a result of not having such abstractions, logical equivalence will force these auxiliaries to be present in any equivalence program. Higher-order quantification can be use to hide predicates and function symbols. If such higher-order quantification is restricted so that operationally, only hiding is specified, then the cost of such higher-order quantifiers within proof search can be small: one only needs to deal with adding new eigenvariables and clauses involving such eigenvariables. On the other hand, the specification of hiding via quantification can allow for novel and interesting proofs of logical equivalence between programs. This paper will present several example of how reasoning directly on a logic program can benefit significantly if higher-order quantification is used to provide abstractions.