What's Necessary to Hide?: 
Modeling Action Verbs 
James F. Alien 
Com purer Science 1)epartmen t 
University of Rochester 
Rochester, NY 14627 
Ahstract 
This paper considers what types of knowledge one 
must possess in order to reason about actions. Rather than 
concentrating on how actions are performed, as is done in 
the problem-solving literature, it examines the set of 
conditions under which an action can be said to have 
occurred. In other words, if one is told that action A 
occurred, what can be inferred about the state of the 
world? In particular, if the representation can define such 
conditions, it must have good models of time, belief, and 
intention. This paper discusses these issues and suggests a 
formalism in which general actions and events can be 
defined. Throughout, the action of hiding a book from 
someone is used as a motivating example. 
I. Introductio, 
This paper suggests a formulation of events and 
actions that seems powerful enough to define a wide range 
of event and action verbs in English. This problem is 
interesting for two reasons• The first is that such a model is 
necessary to express the meaning of many sentences. The 
second is to analyze the language production and 
comprehension processes themselves as purposeful action. 
This was suggested some time ago by Bruce \[1975\] and 
Schmidt \[1975\]. Detailed proposals have been 
implemented recently for some aspects of language 
production \[Cohen, 1978\] and comprehension \[Alien. 
1979\]. As interest in these methods grows (e.g., see \[Grosz, 
1979; Brachman, 1979\]). the inadequacy of existing action 
models becomes increasingly obvious. 
The formalism for actions used in most natural 
language understanding systems is based on case grammar. 
Each action is represented by a set of assertions about the 
• semantic roles the noun phrases play with respect to the 
verb. Such a tbrmalism is a start, but does not explain how 
to represent what an action actually signifies. If one is told 
that a certain action occurred, what does one know about 
how the world changed (or didn't change!). This paper 
attempts to answer this question by oudining a temporal 
logic in which the occurrence of actions can be tied to 
descriptions of the world over time. 
One possibility for such a mechanism is found in the 
work on problem-solving systems (e.g. \[I:ikes and Nilsson, 
197\]; Sacerdoti, 1975\]), which suggests one common 
formulation of action. An acuon is a function from one 
world state to a succeeding world state and is described by 
a set of prerequisites and effects, or by decomposition into 
more primitive actions. While this model is extremely 
useful for modeling physical actions by a single actor, it 
does not cover a large class of actions describable in 
I-ngiish. \[:or instance, many actions seemingly describe 
nml-activity (e.g. standing still), or acting in some non- 
specified manner to preserve a state (e.g. preventing your 
televismn set from being stolen). Furthermore, many 
action descriptions appear to be a composition of simpler 
actions that are simultaneously executed. For instance, 
"Walking to the store while juggling three bails" 
seems to be composed of the actions of 
"walking to the store 
and 
"juggling three bails." 
It is not clear how such an action could be defined 
from the two simpler actions if we view actions as 
functions from one state to another. 
The approach suggested here models events simply as 
partial descriptions of the world over some Lime interval. 
Actions are then defined as a subclass of events that 
involve agents. Thus, it is simple to combine two actions 
into a new action, The new description simply consists of 
the two simpler descriptions hglding over the same 
interval 
The notions of prerequisite, result, and methods of 
performing actions will not arise in this study. While they 
are iraportant for reasoning about how to attain goals, they 
don't play an explicit role in defining when an action can 
be said to have occurred. To make this point clear, 
consider the simple action of turning on a light. 
There are few physical activities that are a necessary 
part of performing this action, Depending on the context, 
vastly different patterns or" behavior can be classified as 
the same action, l;or example, turning on a light usually 
involves Hipping a light switch, but in some circumstances 
it may involve tightening the light bulb (in the basement). 
or hitting the wail (m an old house). Although we have 
knowledge about how the action can be pertbrmed, this 
does nol define what the action is. The key defining 
characteristic of turning on the light seems to be that the 
agent is performing some activity which will cause the 
light, which is off when the action starts, to become on 
when the action ends. The importance of this observation 
is that we could recognize an observed pattern of activity 
as "turning on the light" even if we had never seen or 
thought about that pattern previously. 
The model described here is in many ways similar to 
that of Jackendoff \[1976\]. He provides a classification of 
event verbs that includes verbs of change (GO verbs) and 
verbs that assert a state remaining constant over an 
interval of time (STAY verbs), and defines a 
representation of action verbs of both typesby introducing 
the notion of agentive causality and permission. However, 
Jackendoff does not consider in detail how specific actions 
might be precisely defined with respect to a world model. 
The next two sections of this paper will introduce the 
temporal logic and then define the framework for defining 
events and actions. To be as precise as possible, I have 
remained within the notation of the first order predicate 
calculus• Once the various concepts are precisely defined, 
the next necessary step in this work is to define a 
computaUonally feasible representation and inference 
process, Some of this work has already been done. For 
example, a computational model of the temporal logic can 
be found in Allen \[198.1\]• Other areas axe currently under 
investigation. 
7'7 
/" 
The final section demonstrates the generality of the 
approach by analyzing the action of hiding a book from 
someone. In this study, various other important conceptual 
entities such as belief, intention, and causality are briefly 
discussed. Finally, a definition of.what it means to hide 
something is presented using these tools. 
2. A Temporal l,ogie 
Before we can characterize events and actions, we need 
to specify a temporal logic. The logic described here is 
based on temporal intervals. Events that appear to refer to 
a point in time (i.e., finishing a race) are considered to be 
implicitly referring to another event's beginning or ending. 
Thus the only time points we will see will be the endpoints 
of intervals. 
The logic is a typed first order predicate calculus, in 
which the terms fall into the following three broad 
categories: 
- terms of type TIME-INTERVAL denodng time 
intervals; 
terms of type PROPERTY, denoting descriptions 
that can hold or not hold during a particular time; 
and 
terms corresponding to objects in the domain. 
There are a small number of predicates. One of the most 
important is HOLDS, which asserts that a property holds 
(i.e., is true) during a time interval..Thus 
HOLDS(#,O 
is true only if property p holds during t. As a subsequent 
axiom will state, this is intended to mean that p holds at 
every subinterval oft as well. 
There is no need to investigate the behavior of 
HOLDS fully here. but in Allen \[forthcomingJ various 
functional forms are defined that can be used within the 
scope of a HOLDS predicate that correspond to logical 
connectives and quantifiers outside the scope of the 
HOLDS predicate. 
There is a basic set of mutually exclusive relations that 
can hold between temporal intervals. -Each of these is 
represented by a predicate in the logic..The most 
important are: 
DURING(tl, t2)--time interval tl is fully contained 
within 12, although they may coincide on their 
endpoints. 
BEFORE(tl,t2)--time interval t\] is before interval 12, 
and they do not overlap in any way: 
OVERLAP(tl, t2)--interval tl starts before t2, and 
they overlap; 
MEETS(tl, t2)--interval tl is before interval 12, but 
there is no interval between them, i.e., tl ends 
where t2. starts. 
Given these predicates, there is a set of axioms 
defining their interrelations. For example, there are 
axioms dealing with the transitivity of the temporal 
relationships. Also, there is the axiom mentioned 
previously when the HOI,I)S predicate wa~ introduced: 
namely 
(A.\]) IfOLDS(p.t) & DURING(tl.t) --) HOI,DS(p.tl) 
This gives us enough tools to define the notion of action in 
the next section. 
3. Events and Actions 
In order to define the role that events and actions play 
in the logic, the logical form of sentences asserting that an 
event has occurred must be discussed. Once even~ have 
been defined, actions will be defined in terms of them. 
One suggestion for the logical form is to define for each 
c\[,,~ of events a property such that the property HOI.I)S 
only if the event occurred. This can be discarded 
immediately as axiom (A.\]) is inappropriate for events. If 
an event occurred over some time interval "\['. it does not 
mean that the event also occurred over all subintervals of 
T. So we introduce a new type of object in the logic, 
namely events, and a new predicate OCCUlt. l),y 
representing events as objects in the logic, we have 
avoided the difficulties described in Davidson \[1967\]. 
Simply giving the logical form of an event is only a 
small part of the analysis. We must also define for each 
event the set of conditions that constitute its occurrence. 
As mentioned in the introduction, there seems to be no 
restriction on what kind of conditions can he used to 
define an event except that they must partially describe 
the world over some time interval. 
For example, the event "the ball moving from x to y" 
could be modeled by a predicate MOVE with four 
arguments: the object, the source, the goal location, and 
the move event itself. Thus, 
MOVI'(IlalL x. y. m) 
asserts that m is an event consisting of the ball moving 
from x to y. We assert that this event occurred over time t 
by adding the assertion 
OCCUR(,~ t). 
With these details out of the way. we can now define 
necessary and sufficient conditions for the event's 
occurrence. For this simple class of move events, we need 
an axiom such as: 
(forall object, source, goaLt, e) 
MOVl'(object.source.goal.e) & OCCUR(~t) 
(--) (exists tl.t2) 
OVERLAPS(tl, t) & OVERLAPS(t.t2) & 
BF.FORE(tl.t2) & 
H O LD S(at(object.source). t l ) & 
HOLDS(at(object, goal), t 2 ) 
A simple class of events consists of those that occur 
only if some property remains constant over a particular 
interval (c£ Jackendoffs STAY verbs). For example, we 
may assert in l'nglish 
"The ball was in the room during T.'" 
"The ball remained in the room during T." 
78 
t" 
While these appear to be logically equivalent, they may 
have very different consequences in a conversation. This 
formalism supports this difference. The former sentence 
asserts a proposition, and hence is of the form 
H O L D S(in( BalI, R oom), T) 
while the latter sentence describes an event, and hence is 
of the form 
REMAIN-IN(Bail, Room, e) & OCCURS(e T). 
We may capture the logical equivalence of the two 
with the axiom: 
O'orall b.r,e,O 
REMAIN-IN(b,r,e) & OCCUR(nO 
(=) HOL1)S(in(b.r),O, 
The problem remains as to how the differences 
between these logically equivalent formulas arise in 
context. One possible difference is that the second may 
lead the reader to believe that it easily might not have 
been the case. 
Actions are events that involve an agent in one of two 
ways. The agent may cause the event or may allow the 
event (cf. \[Jackendoff, 1976\]). Corresponding to these two 
types of agency, there are two predicates, ACAUSE and 
ALLOW, that take an agent, an event, and an action as 
arguments. Thus the assertion corresponding to 
"John moved 13 from S to G" 
is 
MO VE(B, G,S, el) & ACA USE(Joh~ el.a1) & 
OCCUR(al.t) 
The axiomadzation for ACAUSE and ALLOW is 
tricky, but Jackendoff provides a reasonable starting set. In 
this paper, I shall only consider agency by causation 
further. The most important axiom about causality is 
(A.2) (forall a,e, act.O 
ACAUSE(a,e.acO & OCCUR(act, t) 
=> OCCUR(cO 
For our purposes, one of the most important facts 
about the ACAUSE relation is that it suggests the 
possibility of intentionality on the part of the agent. This 
will be discussed in the next section. 
Note that in this formalism composition of events and 
actions is trivial. For example, we can define an action 
composition function together which produces an action or 
event that consists of two actions or events occuring 
simultaneously as follows: 
(A.3) (forall a,b.t) 
OCCURS(together(o,b).t) (=) 
OCCURS(c~O & OCCURS(b.t) 
4. What's Necessary to Hide? 
The remainder of this paper applies the above 
formalism to the analysis of the action of hiding a book 
from someone. Along the way, we shall need to introduce 
some new representational tools for the notions of belief, 
intention, and causality, 
The definition of hiding a book should be 
independent of any method by which the action was 
performed, for, depending on the context, the actor could 
hide a book in many different ways. For instance, the 
actor could 
- put the book behind a desk, 
- stand between the book and the other agent while 
they are in the same room, or 
- call a friend Y and get her or him to do one of the 
above. 
Furthermore, the actor might hide ).he book by simply 
not doing something s/he intended to do. I:or example, 
assume Sam is planning to go to lunch with Carole after 
picking Carole up at Carole's office, if, on the way out of 
Sam's office, Sam decides not to take his coat because he 
doesn't want Carole to see it, then Sam has hidden the 
coat from Carole. Of course, it is crucial here that Sam 
believed that he normally would have taken the coat. Sam 
couldn't have hidden his coat by forgetting to bring it. 
This example brings up a few key points that may not 
be noticed from the first three examples. First' Sam must 
have intended to hide the coat. Without this intention (i.e., 
in the forgetting case), no such action occurs. Second, Sam 
must have believed that it was likely that Carole would see 
the coat in the future course of events. Finally, Sam must 
have acted in such a way that he then believed that Carole 
would not see the coat in the future course of events. Of 
course, in this case, the action Sam performed was "not 
bringing the coat," which would normally not be 
considered an action unless it was intentionally not done. 
I claim that these three conditions provide a 
reasonably accurate definition of what it means to hide 
something. They certainly cover the four examples 
presented above. As stated previously, however, the 
definition is rather unsatisfactory, as many extremely 
difficult concepts, such as belief and intention, were 
thrown about casually. 
There is much recent work on models of belief (e.g., 
\[Cohen, 1978; Moore, 1979; Perils, 1981" Haas, 1981\]). l 
have little to add to these efforts, so the reader may 
assume his or her favorite model. I will assume that belief 
is a modal operator and is described by a set of axioms 
along the \[iu~ of Hintikka \[I962\]. The one important 
thing to notice, though, is that there are two relevant time 
indices to each belief; namely, the time over which the 
belief is held, and the time over which the proposition that 
is believed holds. For example. I might believe ~oda.v that 
it rained last weekend. This point wiil be crucial in 
modeling the action of hiding. To introduce some 
notation, let 
"A believes (during To) that p holds (during Tp)" 
be expressed as 
H O LDS(believes(A. holde(p. Tp)), Tb). 
79 
The notion of intention is much less understood than 
the notion of belief. However, let us approximate the 
statement 
"A intends (during Ti) that action a happen (during 
Ta)" 
by 
and 
"A believes (during Ti)that a happen (during Ta)" 
"A wants (during Ti) that a happen (during Ta)" 
This is obviously not a philosophically adequate 
definiuon (e.g., see \[Searle, 1980\]), but seems sufficient for 
our present purposes. The notion of wanting indicates that 
the actor finds the action desirable given the alternatives. 
This notion appears impossible to axiomatize as wants do 
not appear to be rational (e.g. Hare \[\]97\]\]). However, by 
adding the belief that the action will occur into the notion 
of intention, we ensure that intentions must be at least as 
consistent as beliefs. 
Actions may be performed intentionally or 
unintentionally. For example, consider the action of 
breaking a window. Inferring intentionality from observed 
action is a crucial ability needed in order to communicate 
and cooperate with other agents. While it is difficult to 
express a logical connection between action and intention, 
one can identify pragmatic or plausible inferences that can 
be used in a computational model (see \[Allen, 1979\]). 
With these tools, we can attempt a more precise 
definition of hiding. The time intervals that will be 
required are: 
Th--the time of the hiding event; 
Ts--the time that Y is expected to see the book; 
Tbl--the time when X believes Y will see the book 
during "l's, which must be BEFORE "l'h; 
Tb3--the time when X believes Y will not see the 
book during Ts, which must be BEI"ORE or 
DURING Th and AI"I'I'~R Tbl. 
We will now define the predicate 
H I D I.'(agent, observer, object, a~t) 
which asserts that act is an action of hiding. Since it 
describes an action, we have the simple axiom capturing 
agency: 
(forall agent, observer, obJect, act 
H I D l:'(agent, observer, object, act) 
=) (Exists e ACAUSE(agent, e, act))) 
l.et us also introduce an event predicate 
S E l:'(agent, object, e) 
which asserts that e is an event consisting of agent seeing 
the object. 
Now we can define HIDE as follows: 
(forall ag, obs, o.a. 77z, 
HIDl'.'(ag.obs, o,a) & OCCUR(aTh) 
=) (Extsts Ts.Tbl, Tb3,e) 
1) HO LDS(intends(a& occur(a. Th)). Th) 
2) HOLDS(believes(ag, occur(e.Ts)),Tbl) 
3) H O LDS(betieveKa& ~occur(e, Ts)), 7"b3) 
where 
4) SEE(obs, o,e) 
and the intervals Th, Ts, Tb\], Tb3 are related as discussed 
above. Condition (4) defines e as a seeing event, and 
might also need to be within ag's beliefs. 
This definition is lacking part of our analysis; namely 
that there is no mention that the agent's beliefs changed 
because of something s/he did. We can assert that the 
agent believes (between Tbl and Tb3) he or she will do an 
action (between Tbl and Th) as follows: 
(existx" al, el, Tb2 
5) ACAUSlf(a&el,aD 
6) H O LDS(believes(ag, OCC UR(al, Tal)), Tb2) 
where 7"b1 ( Tb2 ( Tb3 and 
Tbl ( 
But this has not 
caused the change in 
(3) are true, asserting 
Tal ( Tit 
captured the notion that belief (6) 
belief from (2) to (3). Since (6) and 
a logical implication from (6) to (3) 
would have no force. It is essential that the belief (6) be a 
key-element in the reasoning that leads to belief (3). 
To capture this we must introduce a notion of 
causality. This notion differs from ACAUSE in many ways 
(e.g. see \[Taylor, 1966\]), but for us the major difference is 
that, unlike ACAUSE, it suggests no relation to 
intentionality. While ACAUSE relates an agent to an 
event, CAUSE relates events to events. The events in 
question here would be coming to the belief (6), which 
CAUSES coming to the belief (3). 
One can see that much of what it means to hide is 
captured by the above. In particular, the following can be 
extracted directly from the definition: 
- if you hide something, you intended to hide it, and 
thus can be held responsible for the action's 
consequences; 
- one cannot hide something if it were not possible 
that it could be seen, or if it were certain that it 
would be seen anyway; 
- one cannot hide something simply by changing 
one's mind about whether it will be seen. 
In addition, there ate many other possibilities related 
to the temporal order of events. For instance, you can't 
hide something by performing an action after ,,he hiding is 
supposed to be done. 
8O 
Conclusion 
I have introduced a representation for events and 
actions that is based on an interval-based temporal logic. 
This model is sufficiently powerful to describe events and 
actions that involve change, as well as those that involve 
maintaining a state. In addition, the model readily allows 
the composition and modification of events and actions. 
In order to demonstrate the power of the model, the 
action of hiding was examined in detail. This forced the 
introduction of the notions of belief, intention, and 
causality. While this paper does not suggest any 
breakthroughs in representing these three concepts, it does 
suggest how they should interact with the notions of time, 
event, and action. 
At present, this action model is being extended so that 
reasoning about performing actions can be modeled. This 
work is along the lines described in \[Goldman, 1970\]. 
Acknowledgements 
The author wishes to thank Jerry Feldman, Alan 
l:risch, Margery I.ucas, and Dan I,',ussell for many 
enlightening comments on previous versions of this paper. 
This research was supported in part by the National 
Science.Foundation under Grant No. IST-80-\]2418, and 
in part by the Office of Naval Research under Grant No. 
N00014-80-C-0197. 
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