A New Deconstructive Logic: Linear Logic (1997)
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Description: Article by V. Danos, J.-B. Joinet and H. Schellinx outlining how linear logic can function as a `mark-up logic' allowing the embedding of a large class of logics in a manner that respects their underlying proof semantics (cf. Nuel Belnap's Display Logic).
CiteSeerX — A New Deconstructive Logic: Linear Logic A New Deconstructive Logic: Linear Logic (1997) Other Repositories/Bibliography by Vincent Danos , Jean-baptiste Joinet , Harold Schellinx , Mathematisch Instituut
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| Page title: | CiteSeerX — A New Deconstructive Logic: Linear Logic |
| Keywords: | CiteSeerX, Vincent Danos, Jean-baptiste Joinet, Harold Schellinx, Mathematisch Instituut |
| Description: | CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The main concern of this paper is the design of a noetherian and confluent normalization for LK 2 (that is, classical second order predicate logic presented as a sequent calculus). The method we present is powerful: since it allows us to recover as fragments formalisms as seemingly different as Girard's LC and Parigot's ¯, FD ([10, 12, 29, 33]), delineates other viable systems as well, and gives means to extend the Krivine/Leivant paradigm of `programming-with-proofs' ([24, 25]) to classical logic; it is painless: since we reduce strong normalization and confluence to the same properties for linear logic (for non-additive proof nets, to be precise) using appropriate embeddings (so-called decorations); it is unifying: it organizes known solutions in a simple pattern that makes apparent the how and why of their making. A comparison of our method to that of embedding LK into LJ (intuitionistic sequent calculus) brings to the fore the latter's defects for these `deconstructive purposes'... |
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