Abstract

Phase models for affine linear logic were independently devised by Lafont [10] and Piazza [15], although foreshadowed by Ono [14]. However, the existing semantics either contain no explicit directions for the construction of models in the general case, or else are forced to resort to additional conditions extending Girard's semantics. We dispense with these extra postulates - at least for the subexponential fragment of this logic - considering structures where the set of antiphases is concretely constructed. Moreover, we show the equivalence of our phase models and the algebraic models of affine linear logic by means of a representation theorem.