Aspect in Ancient Greek - Nijmegen Centre for Semantics

178 Appendix A: The language of Compositional DRTthe conditions of K true: Mx 1 . . .x n(200) γ 1 = . . . γ 2{〈f, f ′ 〉 | f⌊x 1 , . . ., x n ⌋f ′ &f ′ ∈ γ 1 M ∪ . . . ∪ γ m M }The fact that the meaning of a DRS is a relation between assignments isresponsible for the dynamic nature of DRT. CDRT mimics this in type logicby adopting assignments in the object language. In order to do so, the set ofprimitive types (with e the type of regular Mary and John kind of entities,t the type for truth values) is enriched with the types r for registers ands for states. Registers come in two kinds: variable registers, whose contentcan always be changed, and constant registers, which have a fixed inhabitant.States and variable registers are to behave as assignments and variables inpredicate logic or DRT. This is guaranteed by adopting the axiom that in eachstate, each variable register can be updated selectively, i.e. its value can beset to any variable, while the values of other registers can remain unchanged(AX1 below). Another axiom (AX4) guarantees that constant registers havea fixed inhabitant.Once we have registers and states in the language of type logic, functioningas variables and assignments, DRSs can be viewed as abbreviations ofexpressions in this language:(201)abbreviationu 1 . . .u nγ 1. . .γ mfull formλiλj[i⌊u 1 , . . .,u n ⌋j ∧ γ 1 (j) ∧ . . . ∧ γ m (j)]where i and j are variables over states. Note the close similarity with (200).The important difference is that (201) does not give the interpretation of aDRS. DRSs don’t get a direct interpretation. Instead, (201) specifies the fulltype-logical form of the DRS-abbrevation and it is only these type-logical expressionsthat will be assigned an interpretation. The full abbreviation rulesfor DRSs are given in section A.7.Importantly, the merging lemma, as given in (202), still holds under thenew interpretation of DRSs: