linear logic

plural linear logics

1. human sciencesA logic in which two structural rules are missing from its sequent calculus: those for weakening and contraction; which has some extra logical connectives, so that it has both "additive" and "multiplicative" versions of the typical binary connectives and truth constants; and which has a pair of modal, "exponential" operators for resource management, to help make up for the loss of the two structural rules.

   Gentzen also wrote down inference rules suitable for the intuitionistic propositional and predicate calculi. These rules lack the mirror symmetry of the classical case. But in the 1980s, this symmetry was restored by Girard’s invention of ‘linear logic’ [43].

   2009 February 3, John C. Baez with Mike Stay, “Physics, Topology, Logic and Computation: A Rosetta Stone”, in (Please provide the book title or journal name), page 39