Higher-Order Semantics and Extensionality

Journal of Symbolic Logic 69 (4):1027 - 1088 (2004)
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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DOI 10.2307/30041776
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Reinhard Muskens (2005). Sense and the Computation of Reference. Linguistics and Philosophy 28 (4):473 - 504.

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