Linearity 101A Learning Lounge course about Linear Logic issues.
A. Yonezawa: Linear Logic as a paradigm for concurrent programming (I don't find this paper, probably the contributor intended this: ACL - a concurrent linear logic programming paradigm (.ps.Z) -- MaD70).
NB: SSA (single static assignment) forms used internally by some compilers (and remarkably by the .NET Intermediate Representation for programs) is directly related to linearity.
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No, Single-Static Assignment does not make the use of a variable linear, it just makes the variable immutable, and therefore referentially-transparent. However, the dual form of SSA, "SSU" or Static Single Use, where each assignment reaches at most one use, does correspond directly to linearity, and is useful in performing a number of analyses and optimizations related to placement of variable assignments and memory stores.