Linear Logic, Totality and Full Completeness

I give a `totality space' model for linear logic [4], detaking an abstract view of computations on a datatype. The model has similarities with both the coherence space model and game-theoretic models [1, 5], but is based upon a notion of total object. Using this model, I prove a full completeness result, along the lines of the results for game theoretic models in [1] and [5]. In other words, I show that the mapping of proofs to their interpretations (here collections of total objects uniform for a given functor) in the model is a surjection.

• Type: Conference
• Year: 1994
• Where: LICS
• Authors: Ralph Loader
• Keywords: Automated Reasoning, Coherence Space Model, Game Theoretic Models, LICS 1994, Total Objects