By Jean-Yves Girard, Yves Lafont, Laurent Regnier

ISBN-10: 0521559618

ISBN-13: 9780521559614

This quantity supplies an outline of linear good judgment in 5 elements: class concept; complexity and expressivity; evidence thought; facts nets; and the geometry of interplay. The publication encompasses a normal creation to linear good judgment that might be sure this book's use via the amateur in addition to the specialist. Mathematicians and machine scientists will research a lot from this e-book.

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Scott, and A. Scedrov. Bounded linear logic: a modular approach to polynomial time computability. R. J. Scott, editors, Feasible mathematics, pages 195-209, Boston, 1990. Birkhauser. [20] G. Gonthier, M. -J. Levy. The geometry of optimal lambdareduction. In ACM Press, editor, POPL'92, Boston, 1992. Birkhauser. [21] Y. Lafont. The linear abstract machine. Theoretical Computer Science, 59:95-108, 1990. [22] Y. Lafont. From proof-nets to interaction nets. In this volume, 1995. [23] J. Lambek. Bilinear logic in algebra and linguistics.

A obtained from it by a weakening rule is interpreted by the set p* = {x[ ] ; x E 7r*}. 3. A obtained from 1r by a contraction rule is interpreted by the set p* = {x(a + b) ; jab E 7r* A a : b}. 4. A obtained from it by a dereliction rule is interpreted by the set p* = {x[a] ; xa E 7r*}. 6 33 The bridge with intuitionism First the version just given for the exponentials is not the original one, which was using sets instead of multisets. The move to multisets is a consequence of recent progress on classical logic [12] for which this replacement has deep consequences.

It was shown in [1958] that this works for the syntactic calculus even more easily than for intuitionistic logic. First we replace the axiom mAB by the rule of inference f:r->A g:O-*B fµg : FL -- A ®B where fµg = (m&f)&g. This has the form of an introduction rule: the symbol ® is introduced on the right, just as in f§ the same symbol is introduced on the left. In the same way, we replace the axiom ecB by the rule of inference f: A -> A g: I'BA -> C gef : FB/AAO -; C where gef = g&(e& f ). Again, this introduces / on the left, just as f* introduces / on the right.

### Advances in linear logic by Jean-Yves Girard, Yves Lafont, Laurent Regnier

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