Journal of Symbolic Logic

Higher-order semantics and extensionality

Christoph Benzmüller, Chad E. Brown, and Michael Kohlhase

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In this paper we re-examine the semantics of classical higher-order logic with the purpose of clarifying the role of extensionality. To reach this goal, we distinguish nine classes of higher-order models with respect to various combinations of Boolean extensionality and three forms of functional extensionality. Furthermore, we develop a methodology of abstract consistency methods (by providing the necessary model existence theorems) needed to analyze completeness of (machine-oriented) higher-order calculi with respect to these model classes.

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J. Symbolic Logic, Volume 69, Issue 4 (2004), 1027-1088.

First available in Project Euclid: 2 December 2004

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Benzmüller, Christoph; Brown, Chad E.; Kohlhase, Michael. Higher-order semantics and extensionality. J. Symbolic Logic 69 (2004), no. 4, 1027--1088. doi:10.2178/jsl/1102022211.

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