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Higher-order semantics and extensionality

Published online by Cambridge University Press:  12 March 2014

Christoph Benzmüller ,
Chad E. Brown  and
Michael Kohlhase
Christoph Benzmüller
Affiliation:
Department of Computer Science, Saarland University, Saarbrücken, Germany, E-mail: chris@ags.uni-sb.de, URL: http://www.ags.uni-sb.de/~chris
Chad E. Brown
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA, E-mail: cebrown@andrew.cmu.edu, URL: http://www.andrew.cmu.edu/~cebrown/
Michael Kohlhase
Affiliation:
School of Engineering and Sciences, International University Bremen, Bremen, Germany School of Computer Science, Carnegie Mellon University, Pittsburgh, USA, E-mail: m.kohlhase@iu-bremen.de, URL: http://www.cs.cmu.edu/~kohlhase
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Abstract.

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 4 , December 2004 , pp. 1027 - 1088
Copyright
Copyright © Association for Symbolic Logic 2004

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