On adverbs of space and time
Kyle Rawlins (Johns Hopkins University)
The problem I address in a unified way two closely related and unsolved puzzles about Cresswell’s “adverbs of space and time”. The scope puzzle is that some (but not obviously all) sentences
show differential meaning depending on the position (manner, sentential) of the adverb (Cresswell ). This pattern resembles a pattern seen with many adverbs (McConnell-Ginet ;
Ernst ; Rawlins  a.o.), but for this family of adverbs, is often challenging to characterize.
The selectional puzzle is that these adverbs aren’t compatible with all verbs; the distinction seems
to involve aspectual class, and the pattern differs between manner and sentence adverbs. (Statives,
not shown, uniformly exclude adverbs of this type; cf. Katz .) In particular, predicates with
punctual event structure are acceptable with both positions, but activities vary by predicate.
()
Scope puzzle
a. (Class ended.) Slowly, the students left. (≈ the time it took was long)
b. The students left slowly. (≈ their manner of motion was “slow”)
()
Selection puzzle (activities)
a. i. ?? Slowly, Alfonso walked.
!Alfonso walked slowly.
b. i. !Slowly, Alfonso slept.
ii. ?? Alfonso slept slowly. (Katz )
()
Selection puzzle (achievements/semelfactives)
a. ! Alfonso sneezed quickly. (≈ the sneeze was short)
b. ! (Mary glanced at Alfonso.) Quickly, he sneezed. (≈ the time from prior event was
short)
My proposal is that this variety of adverbial modification involves degree modification that
distributes over compositionally available event structure. The point at which the adverb enters
semantic composition determines what sort of event structure will be available, i.e. how it will be
packaged and what can be distributed over. When distribution is not possible, infelicity results
(the distribution constraint). The aspectual constraints in sentential position, I show, match constraints on the structure of narrative discourse (Dowty , “The effect of aspectual class on the
temporal structure of discourse”, L&P ), and follow from the alignment of eventualities in that
kind of discourse (the narrative alignment constraint).
The ratio account My starting point is Cresswell’s  account. On this account, an adverb
like “quickly” in manner position says that the ratio of distance travelled to time, for most of the
smallest temporal subintervals where the predicate still holds, exceeds some contextually provided
standard. In sentential position, the adverb simply says that the time from the closest previous
reference time to the current reference time is short. These meanings are intuitively but not
formally related on the ratio account, leading to the scope puzzle.
A key feature of the account is that the comparison to the standard is distributed throughout
maximal minimal subintervals of the event. This idea is one that must be preserved, but its
form has three problems. First, distribution is built into the adverb in a complicated way; much
following work on distributivity leads to the natural idea of generalizing the distribution property.
Second, distribution to most atomic intervals is not restrictive enough (if I walk down a hall with
 slow footsteps and  fast ones, I have not walked quickly.) Finally, we have already seen that
space/time (manner) adverbs are compatible with many events which involve no distance traveled,
such as (a). (Cresswell acknowledged but did not analyze examples of this type.)
Analysis I take adverbs of space and time to be, at their core, degree functions, following much
work in the adjectival domain (Kennedy , ). Given an event, they return the temporal
length of that event. In the adjectival domain, this function would combine with a degree morpheme that performs comparison with some standard. To account for the differential meaning
effects (how will be made clear shortly), I propose that degree modification in this domain is in
general distributive. That is, the comparison with a standard is distributed across the atoms of
the algebraic part-structure of the event argument. (See Landman  for the version of the
distributive operator D I assume here; AT gives the atoms (if any) of a join semi-lattice.)
()
()
()
quickly = λe . |τ(e)|
(where τ gives the temporal trace of an event)
…D
†
posadv = λP . λe . ∀e 0 ∈ AT(e) : P (e 0 ) < d s
Defined for e only if AT(e) is defined, and where d s is a contextually provided standard.
…
†
[DegP D posadv [AdvP quickly]] = λe . ∀e 0 ∈ AT(e) : |τ(e 0 )| < d s
Defined for e only if AT(e) is defined, and where d s is a contextually provided standard.
…
†
The distribution of all of the manner cases follows directly. Some activities, walking, running,
etc., involve a well-defined set of atoms (e.g. individual steps, approximately), but others, such as
sleeping have no atoms (i.e. they do not characterize an atomic join semi-lattice; cf. Link/Bach).
Distribution is therefore impossible in the second case, as AT(e) is not defined. This parallels
failure of distribution in nominal examples such as *“The water each tasted good.” Achievements(/semelfactives) like “sneeze” form the other limiting case – the event itself is the atom.
What do adverbs of space and time modify when in sentential position? My proposal is
that they still modify eventuality-predicates, but ones that describe potentially longer events with
different algebraic structure. In particular, the structure of the event identified by the VP is “closed
off ” as in collective/group formation on my accounts of plurality. What was previously maximal
now becomes the minimal size for an atom. I take this operation to be performed as a byproduct
of tense/aspect on a Klein/Kratzer account. At this level of event structure, many properties are
constrained by discourse, rather than sentence-semantics. The crucial constraint for us is a version
of Dowty’s  Temporal Discourse Interpretation Principle:
()
()
Narrative alignment constraint
In narrative discourse, sentences must (to the extent possible) characterize events that span
from the prior reference time to the current one.
…
†
Quickly, Alfonso
sneezed
= ∃e : τ(e) < now ∧ AT(e) = {e}∧ ¢
¡ 0
∃e : τ-contains(e, e 0 ) ∧ Ag(e 0 ) = Alf. ∧ sneezing(e 0 ) ∧ ∀e 00 ∈ AT(e) : |τ(e 00 )| < d s
The narrative alignment constraint forces the outer e to span from the reference time of a previous utterance to ref , and consequently the adverb of space and time characterizes the length of
this span. (Note that I differ from standard neo-Davidsonian accounts such as Parsons  in
treating the outer variable as an eventuality, as opposed to an interval.) The constraint also forces
e to be an event (as opposed to a state), something not generally true for other discourse relations.
Therefore sentential space/time adverbs are only guaranteed to be acceptable in narrative contexts, and Dowty’s explanation for the distribution of activities in narrative contexts also explains
the adverb pattern. When statives are good, this is because the space/time adverb leads to an
“inceptive” reading in the manner of Dowty’s “suddenly” examples. Thus this proposal provides
a comprehensive and general account of the behavior of adverbs of space and time.
References
Cresswell, M.: , ‘Adverbs of space and time’. In: F. Guenthner and S. J. Schmidt (eds.): Formal semantics and pragmatics for natural languages. Reidel, pp. –. reprinted in Cresswell
.
Cresswell, M.: , Adverbial Modification. D. Reidel Publishing Company.
Dowty, D.: , ‘The effects of aspectual class on the temporal structure of discourse: semantics
or pragmatics?’. Linguistics and Philosophy , –.
Ernst, T.: , The Syntax of Adjuncts. Cambridge University Press.
Katz, G.: , ‘Event arguments, adverb selection, and the Stative Adverb Gap’. In: E. Lang, C.
Maienborn, and C. Fabricius-Hansen (eds.): Modifying Adjuncts. Mouton de Gruyter.
Kennedy, C.: , Projecting the Adjective: The Syntax and Semantics of Gradability and Comparison. Garland Publishing Inc.
Kennedy, C.: , ‘Vagueness and grammar: the semantics of relative and absolute gradable
adjectives’. Linguistics and Philosophy , –.
Landman, F.: , Events and Plurality. Kluwer Academic Publishers.
McConnell-Ginet, S.: , ‘Adverbs and logical form: A linguistically realistic theory’. Language
, –.
Parsons, T.: , Events in the Semantics of English. Cambridge, MA: MIT Press.
Rawlins, K.: , ‘Unifying ‘Illegally”. In: J. Dölling, T. Heyde-Zybatow, and M. Schäfer
(eds.): Event Structures in Linguistic Form and Interpretation, Language, Context and Cognition.
Mouton de Gruyter, pp. –.