1. Klein’s three-time model
- $UT$ (utterance time): 말하는 시간
- $TT$ (topic time): 이야기하는 대상 시간 (화제가 되는 시간)
- $ET$ (event time): 사건이 일어나는 시간
2. Definitions
- precedence: $I < J \iff \forall t \in I\ \forall t’ \in J\ t < t’$
- inclusion: $I\subset J \iff \forall t\,(t\in I \rightarrow t\in J)$
3. Tenses
| Category | Relation |
|---|---|
| past | $TT < UT$ |
| present | $UT \subset TT$ |
| future | $UT < TT$ |
4. Aspects
| Category | Relation | Expression |
|---|---|---|
| perfective | $ET \subset TT$ | |
| progressive | $TT \subset ET$ | progressive auxiliary be |
| perfect | $ET < TT$ | perfect auxiliary have |
5. 주요 조합
| Category | Relation | Expression |
|---|---|---|
| past perfective | $(TT < UT) \land (ET \subset TT)$ | preterite lexical verb |
| present progressive | $(UT \subset TT) \land (TT \subset ET)$ | is |
| present perfect | $(UT \subset TT) \land (ET < TT)$ | have |
| future perfective | $(UT < TT) \land (ET \subset TT)$ | will |
6. Non-finite clauses
Non-finite clauses는 matrix clause의 $TT$를 물려받는다.
Example.
Having discovered that elliptical orbits fit the observations, he could not reconcile them with his idea.
- tense: $TT_{non-finite} = TT_{matrix}<UT$
- aspect: $ET < TT$
7. Dowty’s aspectual calculus
state verb $\phi$에 대해서는 perfect를 아래와 같이 정의한다: \(\text{AT}(t_0, \text{PERF } \phi) \longleftrightarrow \exists I_{XN} [t_0 \in \text{RightBoundary}(I_{XN}) \wedge \forall I' [I' \subseteq I_{XN} \rightarrow \text{AT}(I', \phi)]].\)