Interpreting Descriptions in Intensional Type Theory

Journal of Symbolic Logic 70 (2):488 - 514 (2005)
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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DOI 10.2178/jsl/1120224725
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Gottlob Frege (1948). Sense and Reference. Philosophical Review 57 (3):209-230.

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