Get Advances in linear logic PDF

By Jean-Yves Girard, Yves Lafont, Laurent Regnier

ISBN-10: 0521559618

ISBN-13: 9780521559614

This quantity provides an summary of linear good judgment in 5 components: class idea; complexity and expressivity; evidence thought; facts nets; and the geometry of interplay. The e-book incorporates a common advent to linear good judgment that might confirm this book's use by means of the amateur in addition to the professional. Mathematicians and desktop scientists will examine a lot from this ebook.

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Extra resources for Advances in linear logic

Sample text

Typically one cannot exclude the existence of a non-deterministic denotational semantics for classical logic, but God knows how to get it ! LC is indeed fully compatible with linear logic : it is enough to add a new polarity 0 (neutral) for those formulas which are not canonically equipped with a structure of correlation space. The miracle is that this combination of classical with intuitionistic features accommodates intuitionistic logic for free, and this eventually leads to the system LU of unified logic, see [13].

Let us end this chapter by yet another refutation of weakening and contraction : 1. If we have a unit with interface t- F, it would be wrong to add another plug A ; such a plug (since we know nothing about the inside of the unit) must be a mock plug, with no actual connection with the unit ... Imagine a plug on which it is written "danger, 220V", you expect to get some result if you plug something with it : here nothing will happen ! LINEAR LOGIC : ITS SYNTAX AND SEMANTICS 39 2. - F, A, A, it would be wrong to merge the two similar plugs into a single one : in real life, we have such a situation with the stereophonic output plugs of an amplifier, which have exactly the same specification.

Up to now, the only completeness is achieved at the level of provability (by phase spaces) which is rather marginal. Typically a complete game semantics would yield winning strategies only for those formulas which are provable. The difficulty is to find some semantics which is not contrived (in the same way that the phase semantics is not contrived : it does uses, under disguise, the principles of linear logic). A non-contrived semantics for linear logic would definitely settle certain general questions, in particular which are the possible rules.

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

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