15-816 Linear Logic
Lecture 3: Unrestricted Hypotheses

After completing purely linear natural deduction by introducing disjunction (external choice), we generalize the hypothetical judgment to allow unrestricted hypotheses. These arise if we can show that a goal can be achieve in any state (or, in other words, can be achieved independently of any linear resources).

This generalization requires a so-called categorical judgment. After this addition, our logic is strong enough so we can directly interpret ordinary logic reasoning (intuitionistic or classical).

As another example we consider the representation of non-deterministic finite automata.

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Frank Pfenning