Linear logic is a resource-sensitive logic in which assumptions cannot in general be copied or discarded. It has distinct multiplicative and additive
conjunctions and disjunctions,
conventionally including the connectives 
and 
. The exponential modalities 
and 
mark formulas for which the usual structural rules of contraction and weakening are
permitted. This control of duplication gives linear logic applications in proof
theory, semantics, and the analysis of computational resources.
Linear Logic
See also
Logic, Proof Theory, Substructural LogicExplore with Wolfram|Alpha
References
Girard, J.-Y. "Linear Logic." Theoret. Comput. Sci. 50, 1-101, 1987. https://doi.org/10.1016/0304-3975(87)90045-4.Cite this as:
Weisstein, Eric W. "Linear Logic." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LinearLogic.html