concrete biclosed monoidal categories

1 Nov 2002

      For an application connected with the syntax-semantics interface in
natural language, I would be grateful for either (1) advice on ways to
complete the following proportion:

 cartesian closed category:
 positive propositional intuitionistic logic:
 heyting semilattice:
 Henkin frame (with products)

 ::

 biclosed (not necessarily symmetric) monoidal closed category:
 noncommutative multiplicative propositional intuitionistic linear logic:
 residuated monoid:
 ?

or (2) a persuasive argument that there is no sensible way to complete
it.

Carl Pollard