This volume contains a selection of papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford. Linearity has been a key feature in several lines of research in both theoretical and practical approaches to computer science. On the theoretical side there is much work stemming from linear logic dealing with proof technology, complexity classes and more recently quantum computation. On the practical side there is work on program analysis, expressive operational semantics for programming languages, linear programming languages, program transformation, update analysis and efficient implementation techniques. Linear logic is not only a theoretical tool to analyse the use of resources in logic and computation. It is also a corpus of tools, approaches, and methodologies (proof nets, exponential decomposition, geometry of interaction, coherent spaces, relational models, etc.) that were originally developed for the study of linear logics syntax and semantics and are nowadays applied in several other fields.
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