Softness of hypercoherences and MALL full completeness

Softness of hypercoherences and MALL full completeness

We prove a full completeness theorem for multiplicative-additive linear logic (i.e. MALL) using a double gluing construction applied to Ehrhard’s ∗-autonomous category of hypercoherences. This is the first non-game-theoretic full completeness theorem for this fragment. Our main result is that every dinatural transformation between definable functors arises from the denotation of a cut-free MALL...

Concurrent Games and Full Completeness

A new concurrent form of game semantics is introduced. This overcomes the problems which had arisen with previous, sequential forms of game semantics in modelling Linear Logic. It also admits an elegant and robust formalization. A Full Completeness Theorem for Multiplicative-Additive Linear Logic is proved for this semantics.

Parallel and serial hypercoherences

It is known that the strongly stable functions which arise in the semantics of PCF can be realized by sequential algorithms, which can be considered as deterministic strategies in games associated to PCF types. Studying the connection between strongly stable functions and sequential algorithms, two dual classes of hypercoherences naturally arise: the parallel and serial hypercoherences. The obj...

Linear Logic, Totality and Full Completeness

I give a ‘totality space’ model for linear logic [4], derived by taking 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 ...

Axioms for De nability and Full Completeness