Tense and Aspect Semantics

Origin. Reichenbach (1947), Vendler (1957), Kamp, Kratzer. Temporal reference. Aspectual classes. Event structure. Foundation of temporal semantics.

Models. Tense locates in time. Aspect views event structure. Reference time mediates. Aktionsart classes. Temporal reasoning.

Formalism.

Reichenbach's three times: S: speech time. R: reference time. E: event time. Relations determine tense.

Tense analysis: Past: E,R < S. Present: S,R,E (simultaneous). Future: S < R,E. Perfect: E < R. "Had left": E < R < S.

Vendler classes (Aktionsart): States: know, love (no internal structure). Activities: run, swim (duration, no endpoint). Accomplishments: build a house (duration + endpoint). Achievements: arrive, die (instantaneous).

Aspectual operators: PROG: progressive (ongoing). PERF: perfect (completed before R). PROG(P)(t) iff t within ongoing P-event. PERF(P)(t) iff P-event completed before t.

Event semantics integration: ∃e[P(e) ∧ τ(e) ⊆ t]. τ(e): temporal trace of e. Event with temporal location. Compositional.

Interval semantics: Times as intervals. Relations: <, ○ (overlap), ⊆. Allen's interval algebra. Temporal reasoning.

Coercion: "John is knowing the answer" (odd). State → activity coercion. Aspectual shift. Interpretive adjustment.

Symbols.

Symbol	Unicode	Meaning
S, R, E	—	speech, reference, event time
τ(e)	—	temporal trace
PROG	—	progressive
PERF	—	perfect

Metatheory. Three-time structure. Aktionsart. Event traces. Aspectual operators.

Applies to. Tense. Aspect. Temporal reasoning. Cross-linguistic.

Limitations. Cross-linguistic variation. Coercion complexity. Interaction effects. Context.