Interpreting Descriptions in Intensional Type Theory

Journal of Symbolic Logic 70 (2):488 - 514 (2005)
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Abstract

Natural deduction systems with indefinite and definite descriptions (ε-terms and ι-terms) are presented, and interpreted in Martin-Löf's intensional type theory. The interpretations are formalizations of ideas which are implicit in the literature of constructive mathematics: if we have proved that an element with a certain property exists, we speak of 'the element such that the property holds' and refer by that phrase to the element constructed in the existence proof. In particular, we deviate from the practice of interpreting descriptions by contextual definitions

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References found in this work

On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Revue Philosophique de la France Et de l'Etranger 89:465-466.
Sense and reference.Gottlob Frege - 1948 - Philosophical Review 57 (3):209-230.
A General Theory of Completeness Proofs.Sh^|^Ocirc Maehara & Ji - 1970 - Annals of the Japan Association for Philosophy of Science 3 (5):242-256.
Intuitionistic Predicate Calculus with ^|^epsilon;-Symbol.Kokio Shirai - 1971 - Annals of the Japan Association for Philosophy of Science 4 (1):49-67.

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