Abstract
We give a Dialectica-style interpretation of first-order classical affine logic. By moving to a contraction-free logic, the translation (a.k.a. D-translation) of a first-order formula into a higher-type ∃∀- formula can be made symmetric with respect to duality, including exponentials. It turned out that the propositional part of our D-translation uses the same construction as de Paiva's dialectica category struck G signℂ and we show how our D-translation extends double struck G signℂ to the first-order setting in terms of an indexed category. Furthermore the combination of Girard's ?!-translation and our D-translation results in the essentially equivalent ∃∀-formulas as the double-negation translation and Gödel's original D-translation.
Original language | English |
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Pages (from-to) | 49-79 |
Number of pages | 31 |
Journal | Theory and Applications of Categories |
Volume | 17 |
Publication status | Published - 2006 Dec 16 |
Keywords
- Categorical logic
- Dialectica interpretation
- Linear logic
ASJC Scopus subject areas
- Mathematics (miscellaneous)