A Weakly - Typed Higher Order Logicwith
نویسنده
چکیده
We deene a higher order logic which has only a weak notion of type, and which permits all terms of the untyped lambda calculus and allows the use of the Y combinator in writing recursive predicates. The consistency of the logic is maintained by a distinction between use and mention, as in Gilmore's logics. We give a consistent model theory and a proof system which is valid with respect to the model theory. We also give examples showing what formulas can and cannot be used in the logic.
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