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HigherOrder Quantification and Proof Search
 In Proceedings of the AMAST confrerence, LNCS
, 2002
"... Logical equivalence between logic programs that are firstorder logic formulas holds between few logic programs, partly because firstorder 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 a ..."
Abstract

Cited by 7 (4 self)
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Logical equivalence between logic programs that are firstorder logic formulas holds between few logic programs, partly because firstorder 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.
Solving for Set Variables in HigherOrder Theorem Proving
 Proceedings of the 18th International Conference on Automated Deduction
, 2002
"... In higherorder logic, we must consider literals with exible (set variable) heads. Set variables may be instantiated with logical formulas of arbitrary complexity. An alternative to guessing the logical structures of instantiations for set variables is to solve for sets satisfying constraints. U ..."
Abstract

Cited by 6 (1 self)
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In higherorder logic, we must consider literals with exible (set variable) heads. Set variables may be instantiated with logical formulas of arbitrary complexity. An alternative to guessing the logical structures of instantiations for set variables is to solve for sets satisfying constraints. Using the KnasterTarski Fixed Point Theorem [ 15 ] , constraints whose solutions require recursive de nitions can be solved as xed points of monotone set functions. In this paper, we consider an approach to higherorder theorem proving which intertwines conventional theorem proving in the form of mating search with generating and solving set constraints.