Interpolation Theorems for Resolution in Lower Predicate Calculus
Journal of the ACM (JACM)
A theorem-proving language for experimentation
Communications of the ACM
Handbook of automated reasoning
A many-sorted calculus based on resolution and paramodulation
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
A many-sorted resolution based on an extension of a first-order language
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
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This work demonstrates how a first-order logical system with more than one type of individual variable can be used to prove theorems in higher-order logic. Certain of the types are considered to be individuals while other types are treated as predicates and functions. For each pair of types i,j where type i objects are to be predicates over type j objects, a special 2-place predicate symbol P is included which acts as a graph, i.e. P(a,b) iff a(b). The lambda operator could be implemented as a set of comprehension axioms. However, since the axioms needed for a particular theorem are not generally known ahead of time and the inclusion of axioms in a theorem-proving program usually decreases efficiency, a new rule of inference, called naming, is proposed instead. Completeness of the resulting procedure is shown for a small class of higher-order problems. Some suggestions for computer implementation are given.