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<Paper uid="P81-1017">
  <Title>What's Necessary to Hide?: Modeling Action Verbs</Title>
  <Section position="4" start_page="78" end_page="79" type="metho">
    <SectionTitle>
4. What's Necessary to Hide?
</SectionTitle>
    <Paragraph position="0"> 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.</Paragraph>
    <Paragraph position="1"> 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 &amp;quot;not bringing the coat,&amp;quot; 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.</Paragraph>
    <Paragraph position="2"> There is much recent work on models of belief (e.g., \[Cohen, 1978; Moore, 1979; Perils, 1981&amp;quot; Haas, 1981\]). 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 &amp;quot;A believes (during To) that p holds (during Tp)&amp;quot; be expressed as H O LDS(believes(A. holde(p. Tp)), Tb).</Paragraph>
    <Paragraph position="3">  The notion of intention is much less understood than the notion of belief. However, let us approximate the  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.</Paragraph>
    <Paragraph position="4"> 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 &amp;quot;l's, which must be BEFORE &amp;quot;l'h; Tb3--the time when X believes Y will not see the book during Ts, which must be BEI&amp;quot;ORE or DURING Th and AI&amp;quot;I'I'~R Tbl.</Paragraph>
    <Paragraph position="5"> 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.</Paragraph>
    <Paragraph position="6"> Now we can define HIDE as follows: (forall ag, obs, o.a. 77z,</Paragraph>
    <Paragraph position="8"> 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.</Paragraph>
    <Paragraph position="9"> 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&amp;quot; al, el, Tb2  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).</Paragraph>
    <Paragraph position="10"> 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.</Paragraph>
    <Paragraph position="11"> 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.</Paragraph>
    <Paragraph position="13"> I have introduced a representation for events and actions that is based on an interval-based temporal logic.</Paragraph>
    <Paragraph position="14"> 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.</Paragraph>
    <Paragraph position="15"> 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.</Paragraph>
    <Paragraph position="16"> 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 \[Goldman, 1970\].</Paragraph>
  </Section>
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