Tense and Aspect Semantics

Origin. Reichenbach, Elements of Symbolic Logic (1947), §51, for the three-time analysis; Vendler, "Verbs and times" (Philosophical Review 66, 1957), for the four aspectual classes; Prior's Time and Modality (1957) and Past, Present and Future (1967) for the operator treatment; Kamp's dissertation (UCLA, 1968) for Since and Until; Partee (1973) for the argument that tense is anaphoric; Dowty's Word Meaning and Montague Grammar (1979) for the imperfective paradox; Krifka (1989, 1998) for the mereology of events and incremental themes; Klein's Time in Language (1994) for Topic Time.

Models. Tense locates a situation relative to the moment of speech, but not directly: Reichenbach interposes a reference time, and the perfect is what separates it from the event time. Aspect is a different dimension — not where the situation is but how it is viewed, whether as a bounded whole or from inside — and this is cut across by Aktionsart, the lexical event type of the predicate itself. The modern implementations run through events rather than instants: a verb denotes a set of events, a temporal trace function maps an event to the interval it occupies, and tense and aspect constrain that interval. Times are taken as intervals rather than points, which is what makes the durative classes and the progressive statable.

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.

Tense as anaphora (Partee 1973): "I didn't turn off the stove" is neither ¬∃t<now nor ∃t<now¬. The first is too strong, the second trivially true. The past tense picks out a contextually given time, like a pronoun.

The imperfective paradox (Dowty 1979): "John was crossing the street" does not entail "John crossed the street." So PROG cannot be an interval-inclusion operator over the completed event. Dowty's repair: PROG(φ) at t iff φ is completed in every inertia world — those where the event runs to its normal end. Landman (1992): continuation branches instead. Either way, PROG is modal.

Quantization and telicity (Krifka): P is quantized iff no proper part of a P-event is a P-event. "Build a house" is quantized; "run" is not. The incremental theme maps event parts homomorphically onto object parts, which is why "eat the apple" is telic and "eat apples" is not.

Interval algebra (Allen 1983): Thirteen jointly exhaustive, pairwise disjoint relations between intervals. Consistency of a network is NP-complete (Vilain and Kautz 1986). The point algebra is polynomial; ORD-Horn is the maximal tractable subclass (Nebel and Bürckert 1995).

Symbols.

Metatheory. Kamp's theorem (1968) is the central expressiveness result: Since and Until are expressively complete for the first-order theory of time over Dedekind-complete linear orders, though not over arbitrary orders, where further operators are needed. Partee (1973) established that tense is not quantificational: "I didn't turn off the stove" has no reading under either scoping of negation and a Priorean past operator, so the tense must be anaphoric to a contextually supplied time. Dowty (1979) showed the progressive cannot be extensional, since it does not entail completion, and repaired it with inertia worlds — Landman (1992) with continuation branches — making PROG modal on either account. Krifka derives telicity rather than stipulating it: quantization of the object plus an incremental-theme homomorphism yields a quantized event predicate. Temporal reasoning over Allen's thirteen interval relations is NP-complete (Vilain and Kautz 1986), with ORD-Horn the maximal tractable subclass (Nebel and Bürckert 1995).

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

Limitations. Reichenbach's schema both over- and undergenerates: it yields configurations no language expresses while collapsing distinctions that languages do mark, and Comrie (1985) showed the future perfect and the future-in-the-past need more structure than three points allow. The reference time has no diagnostic independent of the tense forms it was introduced to explain. Vendler's classes are not properties of verbs but of verb phrases, so the classification is compositional and its lexical statement is at best a default; the coercion rules that repair mismatches are unconstrained and can accommodate anything. The perfective–imperfective opposition does not align with the Aktionsart classes across languages, so the two-dimensional picture is not a typological universal. PROG's modal base is stipulated, and inertia worlds have no independent characterization.

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