Abstracts.2018.LinLog

Fine Structure of Linear Logic

by Nachiappan Valliappan

Linear logic is a fine-grained refinement of traditional (classical and intuitionistic) logics. In a traditional proof system, for example, we can prove that A ⇒ A ∧ A because our proof system allows us to make arbitrarily many “copies” of A. A linear proof system, on the other hand, restricts this arbitrary usage and provides a more fine-grained system for proofs. In specific, linear logic restricts use of the so-called “structural rules”. As a result, it exposes a number of properties about proofs themselves, and helps us understand the role of structural rules in traditional proof systems. In this talk, we’ll put on our proof theorist hats and obsess over the structural aspects of linear logic. If time permits, we will also visit the categorical interpretation of the “multiplicative” fragment of linear logic.

Notes:

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