Institut
de Mathématiques de Luminy
Abstracts : publications 2000 
Bucciarelli Antonio and
Ehrhard Thomas We study the notion of logical relation
in the coherence space semantics of multiplicativeadditive linear logic
. We show that, when the groundtype logical relation is "closed under
restrictions", the logical relation associated to any type can be seen
as a map associating facts of a phase space to families of points of
the web of the corresponding coherence space. We introduce a sequent
calculus extension of whose formulae denote these families of points.
This logic (where I is a set of indexes) admits a truthvalue semantics
in the previously mentioned phase space, and this truthvalue semantics
faithfully describes the logical relation model we started from. Then
we generalize this notion of phase space, we prove a truthvalue completeness
result for and we derive from any phase model of a denotational model
for . Using the truthvalue completeness result, we obtain a weak denotational
completeness result based on this new denotational semantics.
