Modified Realizability Interpretation of Classical Linear Logic

This paper presents a modified realizability interpretation of classical linear logic. The interpretation is based on work of de Paiva (1989), Blass (1995), and Shirahata (2006) on categorical models of classical linear logic using Godel's Dialectica interpretation. Whereas the Dialectica categories provide models of linear logic, our interpretation is presented as an endo-interpretation of proofs, which does not leave the realm of classical linear logic. The advantage is that we obtain stronger versions of the disjunction and existence properties, and new conservation results for certain choice principles. Of particular interest is the simple branching quantifier used in order to obtain a completeness result for the modified realizability interpretation.