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Multiplicatives. (English) Zbl 0667.03046
Rend. Semin. Mat., Torino Fasc. Spec. 1987, 11-33 (1987).
This is one of the interim reports by the author on developments of (what he calls) linear logic explained by the reviewer at length in his review of the author’s paper in Theor. Comput. Sci. 50, 1-102 (1987; Zbl 0625.03037). Though the theorems themselves are not particularly substantial they are enough to help remember the relatively large new vocabulary in both algebraic and computational terms. As a corollary of that vocabulary a number of relations between linear logic and the other subjects become apparent to the reader. But those noticed so far by the reviewer do not contribute significantly to any of the three subjects involved. This agreeable paper may be more rewarding for the author if, in future, it helps him remember his current expectations of linear logic, and thus compare them with a more consolidated form of this subject; cf., for example, V. Danos and L. Regnier, The structure of multiplicatives [Arch. Math. Logic 28, 181-203 (1989].
Reviewer: G.Kreisel

03F99 Proof theory and constructive mathematics
03B70 Logic in computer science