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Dialectica Categories and Games with Bidding

Author Jules Hedges

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Jules Hedges

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Jules Hedges. Dialectica Categories and Games with Bidding. In 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. 89-110, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.TYPES.2014.89

Abstract

This paper presents a construction which transforms categorical models of additive-free propositional linear logic, closely based on de Paiva's dialectica categories and Oliva's functional interpretations of classical linear logic. The construction is defined using dependent type theory, which proves to be a useful tool for reasoning about dialectica categories. Abstractly, we have a closure operator on the class of models: it preserves soundness and completeness and has a monad-like structure. When applied to categories of games we obtain 'games with bidding', which are hybrids of dialectica and game models, and we prove completeness theorems for two specific such models.

Subject Classification

Keywords
  • Linear logic
  • Dialectica categories
  • categorical semantics
  • model theory
  • game semantics
  • dependent types
  • functional interpretations

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