Abstract
Simple type theory is a higher-order predicate logic for reasoning about truth values, individuals, and simply typed total functions. We present in this paper a version of simple type theory, called PF *, in which functions may be partial and types may have subtypes. We define both a Henkin-style general models semantics and an axiomatic system for PF *, and we prove that the axiomatic system is complete with respect to the general models semantics. We also define a notion of an interpretation of one PF * theory in another. PF * is intended as a foundation for mechanized mathematics. It is the basis for the logic of IMPS, an Interactive Mathematical Proof System developed at The MITRE Corporation.
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