From Phase Semantics to Base-extension Semantics (and back) (opens in new tab)

Linear logic admits a wide range of semantic presentations reflecting its resource-sensitive notion of consequence. One well-known example is phase semantics: an algebraic semantics in which formulas are interpreted in phase spaces, consisting of a commutative monoid and a fixed subset, with respect to which an orthogonality relation is defined. A rather different and much more recent approach is given by base-extension semantics, which defines ...