• Corpus ID: 16799964

Functorial Semantics for Higher-order Logic Dissertation Abstract

  title={Functorial Semantics for Higher-order Logic Dissertation Abstract},
  author={Steve Awodey},
This dissertation investigates what may be termed the model theory of higher-order logic using the methods of category theory. Of course, there is no such eld of logic as \higher-order model theory," and so our rst concern in chapter I will be to specify the basic objects under investigation, viz. higher-order logical theories and their models. This is a fairly straightforward generalization|in two diierent directions|of the familiar corresponding notions for rst-order logic: the notion of a… 
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In the article presented, probabilistic programming is a programming in which the probabilities of the values of the variables are of interest, and category theory is used for construction of type theory and of the logical system.



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  • Philosophy, Mathematics
    Bulletin of the Australian Mathematical Society
  • 1972
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  • 1988

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  • The logic of topoi, Handbook of Mathematical Logic
  • 1977