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A partial functions version of Church's simple theory of types

Published online by Cambridge University Press:  12 March 2014

William M. Farmer
William M. Farmer*
Affiliation:
The Mitre Corporation, Bedford, Massachusetts 01730
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Abstract

Church's simple theory of types is a system of higher-order logic in which functions are assumed to be total. We present in this paper a version of Church's system called PF in which functions may be partial. The semantics of PF, which is based on Henkin's general-models semantics, allows terms to be nondenoting but requires formulas to always denote a standard truth value. We prove that PF is complete with respect to its semantics. The reasoning mechanism in PF for partial functions corresponds closely to mathematical practice, and the formulation of PF adheres tightly to the framework of Church's system.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 3 , September 1990 , pp. 1269 - 1291
Copyright
Copyright © Association for Symbolic Logic 1990

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