"She was crossing the street" does not entail "She crossed the street." What feature of formal aspect semantics explains this inference gap?
AThe progressive is in past tense while the simple past is in present perfect, creating a temporal mismatch
BThe progressive operator requires only that reference time R fall within the event interval, not that the interval reaches its culmination — so the event may have been interrupted
CProgressive aspect in English marks events as hypothetical or counterfactual rather than actual
DThe sentence lacks the perfect structure that would assert event completion
This is the imperfective paradox. The progressive 'was crossing' asserts that R (reference time) falls inside the event interval — the crossing is in progress at that moment — but does NOT require the interval to run to its culmination. The woman may have been hit by a car partway through, making 'was crossing' true but 'crossed' false. By contrast, perfective 'crossed' presents the event as a completed whole. This difference is about internal temporal structure (aspect), not tense, and it is why formal semantics needs both dimensions.
Question 2 Multiple Choice
In Reichenbach's three-time analysis, how are S (speech time), E (event time), and R (reference time) ordered in the sentence "She had left before he arrived"?
AE = R = S — all three coincide at the utterance moment
BS precedes E, E precedes R — speech is before the leaving, which is before the arrival
CE precedes R, R precedes S — the leaving is before the arrival, and the arrival is before speech time
DR precedes E, E precedes S — the reference point is before the event, which is before speech time
The past perfect signals E < R < S. The event (leaving) is prior to R, the reference time anchored to 'when he arrived,' which is itself prior to S (speech time). This three-way ordering explains why the past perfect feels 'doubly past' — it marks distance from a past perspective point, not just from the present. Reichenbach's framework captures this elegantly: different perfect and past constructions reflect different orderings of E, R, and S, not just different distances from speech time.
Question 3 True / False
The same event can be described using either perfective or progressive aspect, and the choice of aspect changes how the event's temporal structure is presented without changing which event occurred.
TTrue
FFalse
Answer: True
Aspect is about viewpoint, not about changing the world. The same crossing event can be described as 'she crossed the street' (perfective: the event is presented as a completed whole, viewed from outside) or 'she was crossing the street' (progressive/imperfective: R is inside the event interval, viewed from within). The event itself is the same; what differs is the temporal perspective. This viewpoint distinction — not a difference in which event happened — is what grammatical aspect formally captures.
Question 4 True / False
In formal semantics, tense and aspect are equivalent — both locate an event in time relative to the utterance moment, just with different names.
TTrue
FFalse
Answer: False
Tense and aspect are distinct dimensions. Tense locates events relative to speech time S (E before S = past; E = S = present; E after S = future). Aspect characterizes the internal temporal structure of events — whether they are presented as completed wholes (perfective) or as processes viewed from within (imperfective/progressive), and whether lexical endpoints are relevant. The same tense can combine with different aspects ('she crossed' vs. 'she was crossing'), and the same aspect appears in different tenses ('she was crossing' vs. 'she is crossing'). Neither subsumes the other; formal semantics requires both.
Question 5 Short Answer
Explain how Aktionsart (lexical aspect) interacts with grammatical aspect, and give an example showing why this interaction matters for truth conditions.
Think about your answer, then reveal below.
Model answer: Aktionsart is the inherent temporal structure encoded in verb meaning: states (no endpoint), activities (no culmination), accomplishments (process + telos), achievements (punctual). Grammatical aspect overlays a viewpoint on this structure. The interaction produces different truth conditions: 'She walked to the store' (accomplishment + perfective) entails arrival because the telos is included in the completed event; 'She was walking to the store' (accomplishment + progressive) does not entail arrival because the progressive places R inside the event without requiring culmination — the telos is suspended. 'She walked' (activity + perfective) entails no specific endpoint because the activity verb encodes none.
These differences in entailment are systematic consequences of how aspect operators compose with lexical event structures, not arbitrary quirks of English idiom. This is why formal semantics needs both Aktionsart and grammatical aspect as separate compositional components — and why cross-linguistic data (e.g., Slavic perfective/imperfective distinctions) reveals the same underlying structure in typologically diverse languages.