2.3 State and event-type reification
The method of temporal arguments encounters difficulties if it is
desired to model
aspectual distinctions between, for example,
states, events and processes. Propositions reporting states (such as
“Mary is asleep”) have
homogeneous temporal incidence, in that
they must hold over any subintervals of an interval over which they
hold (e.g., if Mary is asleep from 1 o'clock to 6 o'clock then she is
asleep from 1 o'clock to 2 o'clock, from 2 o'clock to 3 o'clock, and so
on). By contrast, propositions reporting events (such as “John walks to
the station”) have inhomogeneous temporal incidence; more precisely,
such a proposition is not true of
any proper subinterval of an
interval of which it is true (e.g., if John walks to the station over
the interval from 1 o'clock to a quarter past one, then it is not the
case that he walks to the station over the interval from 1 o'clock to
five past one — rather, over that interval he walks part of the
way to the station).
The method of state and event-type reification was introduced to
cater for distinctions of this kind. It is an approach that has been
especially popular in Artificial Intelligence, where it is particularly
associated with the name of James Allen, whose influential paper (Allen
1984) is often cited in this connection. In this approach, state and
event types are denoted by terms in a first-order theory; their
temporal incidence is expressed using relational predicates “Holds” and
“Occurs”, as for example,
Holds(Asleep(Mary), (1pm, 6pm))
Occurs(Walk-to(John, Station), (1pm, 1.15pm))
where terms of the form (
t,
t′) denote time intervals in the
obvious way.
The homogeneity of states and inhomogeneity of events is secured by
axioms such as
∀s, i, i′(Holds(s, i) & In(i′, i) →
Holds(s, i′))
∀e, i, i′(Occurs(e, i) & In(i′, i) →
¬Occurs(e, i′))
where “In” expresses the proper subinterval relation.
