Discourse semantics (DSx) is based on the fact that the interpretation of uttered sentences is dependent on and co-determined by the information stored in a specialized middle-term cognitive memory called discourse domain (D). DSx studies the structure and dynamics of Ds and the conditions to be fulfilled by D for proper interpretation. It does so in the light of the truth-conditional criteria for semantics, with an emphasis on intensionality phenomena. It requires the assumption of virtual entities and virtual facts. Any model-theoretic interpretation holds between discourse structures and pre-established verification domains.