Linear logic - Wikipedia
Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter. [1]
Linear Logic - Stanford Encyclopedia of Philosophy
2006年9月6日 · Linear logic is a refinement of classical and intuitionistic logic. Instead of emphasizing truth, as in classical logic, or proof, as in intuitionistic logic, linear logic emphasizes the role of formulas as resources.
Introduction to Linear Logic and the Identity of Proofs - GitHub …
Our focus today will be on what linear logic is, why it exists and how it relates to both computation and something called the identity of proofs. You should know some basic (classical) logic. Basically, you need to understand what these symbols mean: ∨, …
Linear logic is a generalization of “ordinary” logic in such a way that it becomes “resource conscious”. Notion of duality, polarity, decomposition of (say) intuitionistic propositional logic. TODO: Pottier’s recent work on state. TODO: Wadler, Pfenning’s recent work on session types.
Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control.
Linear logic is not an alternative logic ; it should rather be seen as an exten-sion of usual logic. Since there is no hope to modify the extant classical or intuitionistic connectives 1, linear logic introduces new connectives. if A and A ) B, then B, but A still holds.
Introduced by Jean-Yves Girard in 1987. Classical logic: is my formula true? Intuitionistic logic: is my formula provable? Linear logic is a bit di erent. (A B)? (A & B)? A? B? A? B? be a vending machine that accepts rubles and dispenses packs of rolos, and let S be a vending machine that accepts shillings and dispenses packs of softmints.
Linear logic has been described as a logic of state or a resource-aware logic. Formally, it arises from complementing the usual notion of logical assump- tion with so-called linear assumptions or linear hypotheses.
Classical logic is about truth, intuitionistic logic is about proofs, now linear logic (LL) is about resources1. In both classical and intuitionistic logics, the structural rules of contrac-tion and weakening are admissible. This allows us to work with either an additive calculus or a multiplicative one.
In this lecture we present classical linear logic and then show that we can easily interpret it intuitionistically. Briefly, classical linear logic can be modeled intuitionistically as deriving a contradiction from linear assump-tions. This is shown via a so-called double-negation translation.
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