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occurrence that may be included in the description.
For example, if we knew that John killed some
particular snake in an actual event, then one
qualification of that event is the weapon used by
John, which may be a stick or a gun. Since many
such qualifications may arise for actual events,
Davidson suggested reifying the event in such a way
that any other qualifier for the event may be added.
For example, the event John killed the snake may be
represented by:
∃e. Kill (john, snake, e)
As such a qualifier that asserts that he used a
weapon like a gun, may be added with a function
weapon applied to the event e thus:
∃e. Kill (john, snake, e) ∧ weapon (e) = gun
Galton likened, Davidson’s e term to Situational
Calculus’ term s. We believe this to be a more
accurate comparison than Vila’s likening of situation
terms to time terms in the method of temporal
arguments (MTA) (Haugh, 1987). This is because
both situational terms and event terms are acted
upon by potentially many functions in the original
theory, which is not necessarily the case for time
terms in MTA (In the case of situational terms the
functions are fluents returning boolean values).
(Galton, 1991) reckoned that instantiation of
events can be achieved by introducing Davidson
style event variables. Thus, by Galton’s proposal, to
assert that Mary kissed John at noon, one would
write:
∃e. Kiss (mary, john, e) ∧ Occurs (e, noon)
In the above formula, e is to be regarded as an event
token. Galton claims that this might be viewed as a
means of syntactically “unreifying” Allen’s reified
logic i.e. doing away with the need to treat formulae
like kiss (mary, john) as terms, as Allen did. He also
notes that causation is easier to express in this new
way. He claims that there is no loss of expressive
power as a result of unreifying Allen’s formulae in
this way. Interestingly, (Allen, 1991), Allen and
(Fergusson, 1994) and (Fergusson, 1995) have since
used Davidson’s instantiation technique in
representing actual actions in a planning system.
However the need to retain action types is realized,
since it enables one to express the fact of an agent
trying to carry out an action.
Galton also criticized the reification of what he
referred to as “state types” in (Kowalski and Sergot,
1986)’s Event Calculus, EC. Kowalski and Sergot
did reify event tokens and state types. For example
the fact that person x travelled to place y is an event
token that initiates the state type of x being in place
y is rendered in EC as:
Travel (x, y, e) ⇒ Initiates (e, in (x, y))
Galton would rather have the consequent part of the
above rendered:
∃s. (Initiates (e, s) ∧ In (x, y, s))
where s is a state token.
(Vila and Reichgelt, 1996) while agreeing with the
need to admit event/state tokens as objects into a
theory instead of types, criticized Galton’s work on
the basis of the fact that Galton did not actually
define a full-fledged theory, but rather gave a set of
schemas for generating a theory. This is particularly
obvious in Galton’s definition of event causation
which goes thus:
∀e
1
, e
2
. Ecause (e
1
, e
2
) ⇔
E (e
1
) ∧ E′ (e
2
) ∧ Occurs (e
1
, i
1
) ∧ Occurs (e
2
, succ
(i
1
)) ∧ ∀i, e. (E (e) ∧ Occurs (e, i) ⇒ ∃e′. (E′(e′)
∧ Occurs (e, succ(i)) )
In this definition, E and E′ are not actual predicates
but placeholders for actual predicates. As such the
above definition is some sort of schema and not an
actual axiom. We note here that succ is a function
returning time intervals, and that what is referred to
as succ (i) is actually referred to as i+1 by Galton,
but the basic ideas are the same.
We believe this same accusation by Vila and
Reichgelt, may be made against the result of
Bacchus et al’s work in unreifying Shoham’s theory
into MTA (i.e. Method of Temporal Arguments)
formulae (Haugh, 1987). They observed rightly that
nothing in Galton’s theory prevents an event token
from occurring at two different times. The reified
theory presented in (Akinkunmi, 2000) demonstrates
this oversight in Galton’s proposal by using
Davidson’s syntax for reifying both event types and
event tokens, and then using a specific logical axiom
which rules out duplicated occurrences of individual
tokens in order to clearly define the difference
between types and tokens.
(Vila and Reichgelt, 1996) thus presented a full-
fledged reified theory first order theory, with
formally defined semantics. The formulae reified are
assumed to be from a first-order. In the new theory,
each n-place predicate of the initial logic becomes
an n+2 place function in the reified logic, the 2
additional sorts being time sorts. Hence a function f
(x, y, t
1
, t
2
) returns a token of type f (x, y) which
starts at time point t
1
and ends at time point t
2
. They
also had 1-place predicates HOLDS and OCCURS
which are similar in usage to Allen’s Holds and
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