A Formal Account of Self-Knowledge and Action

In this paper, we propose a formal theory of knowledge and action that accommodates in dexical knowledge and reflects the dependence of action upon i t . The model-theoretic semantics of belief given characterizes an agent's belief state not only in terms of the ways the wor ld might be if his beliefs are t rue, but also in terms of how the wor ld must look f rom his perspective. We then propose a specification of the condit ions under which an agent is able to achieve a goal by doing an action that does not require the agent to know in an absolute sense who he is or what t ime it is. Final ly, we show through an example how actions can be characterized in an agent-relative way w i th in the theory, so as to avoid requir ing the agent to know which objects are acted upon, and how such a characterization can be used to prove that an agent is able to achieve a goal by doing an action if he knows certain facts. 1 I n t r o d u c t i o n Doing all but the most basic actions requires knowledge. For example, in order to call somebody, one needs to know his phone number. Doing an action may have the effect that one acquires some significant new knowledge. The most penetrat ing theory of the relationship between knowledge and action that addresses art i f ic ial intelligence (A I ) concerns is that of Moore [1985]. His framework is essentially an encoding in ordinary firstorder logic of the possible-world semantics of the combinat ion of first-order dynamic logic w i th an S4 modal logic of knowledge. The central result of Moore's work is a defin i t ion of the condit ions under which an agent is able to achieve a goal by doing an action ( C A N ) , where abi l i ty is understood as requir ing the agent to know enough to achieve the goal, rather than it being jus t physically possible. The defini t ion makes use of the fact that actions are. represented by a type of term and that , since we are in a modal framework, we can distinguish between the action description or concept corresponding to an action term and the sequence of pr imi t ive actions denoted by the term in a part icular possible wor ld. In part icular, it makes sense to talk about an agent knowing what an action description is or an agent having de re knowledge of an act ion. Th is not ion is impor tant because an agent may well know that an action described in a given way achieves his goal w i thout being able to do it because he does not know what pr imi t ive actions the description denotes. The possible-world semantics' account of de re knowl edge is that an agent a knows of x that it is  in wor ld w i f f in all worlds compatible w i th what a knows in wy x is . Fol lowing H in t ikka [1962], knowing who /wha t 6 is is taken to be equivalent to knowing of some x that it is 9. This does not however say much about what is actual ly required for an agent to have de re knowledge; the quest ion is recast into that of what is required for the same indiv idual to exist in dist inct epistemically possible worlds. Actual ly , Moore uses a subst i tut ional interpretat ion of quantifiers, but since r ig id designators are subst i tuted for variables, this has l i t t le effect on the issue. There has been much philosophical debate on this question but the common answer in AI circles has been that knowing who someone is requires having a standard name for that person and simi lar ly for knowing-what [Konolidge, 1986, Levesque, 1984]. Moore [1985J is not very clear as to whether he actually holds this view, but his assertion that " in describing standard identifiers we assumed that everyone knew what they referred to " seems to indicate that this is the case. The account works well for some kinds of objects (e.g. phones) and some tasks (e.g. quest ion answering) but requires some serious stretching in other contexts; for example, what are standard names for a mobile vision-equipped robot? Moore's definit ion of C A N is recursive and goes as follows: an agent is able to achieve a goal by doing an action (e.g. call ing a person) iff either the agent knows what the action is (e.g. knows what dial ing the person's number amounts to) and knows that doing the action would result in the goal being satisfied, or the agent knows what an in i t ia l action is (e.g. knows what looking up the person's number in the phone book amounts to) and knows Moore states that "knowing what action is referred to by an action description means having a rigid designator for the action described . . . a rigid designator for an action must be an executable description of the action". 1 think that formal study of the relationship between knowledge and action holds potential for improving our understanding of this and other epistemological questions. 868 Planning, Scheduling, Reasoning About Actions t ha t his do ing th is i n i t i a l act ion results in h i m being able to achieve the goal by doing some subsequent act ion (e.g. d ia l ing the person's number) . Note tha t the agent is required to know who he is and wha t the i n i t i a l act ion is. The recursive case of the def in i t ion captures the fact t ha t the agent need not i n i t i a l l y know a l l the actions tha t make up a successful p lan as long as he knows tha t he w i l l know wha t to do next at each step of his p lan . T h e only way to ta lk about t ime is th rough the dynamic logic operators. Statements t ha t are not in the scope of a dynamic logic operator may be thought to be about the current t ime . 3 One prob lem w i t h Moore's def in i t ion of ab i l i t y is t ha t i t ignores the fact t ha t much of the knowledge required for act ion is indexical or de se rather t han s imp ly de re. For example, if I am at a par ty , I can go and ta lk to the person s tand ing by the punch bowl even i f I don ' t know who tha t person is; nor do I need to know her la t i tude and long i tude or any other object ive specif icat ion of where she is; a l l I need to know is roughly where tha t person is relative to me. If you are tempted to th ink t ha t one knows who a person is as soon as one knows wha t she looks l ike, imagine i t ' s a costume par ty . S imi lar ly , one can go for lunch now w i t h o u t knowing what t ime it is. Moreover, one can do bo th of these actions w i t h o u t know ing who one is — for instance if one is amnesiac. The fact tha t percept ion also yields most ly indexical knowledge is an add i t iona l reason for deal ing w i t h i t . I t has also been argued tha t indexical representat ions carry signif icant efficiency advantages [Agre and Chapman , 1987]. I t is arguable tha t al l aspects of the index ica l i ty of bel ief may be reduced to two pr imi t i ves : 'he h i m s e l f or T, which stands for the agent of the belief, and ' the current t i m e ' or 'now ' , wh ich stands for the t ime of the belief ( th is seems to be the view of Lewis [1979]). 'Here ' can be taken to stand for ' the locat ion of he h imsel f now' . 5 Demonstrat ives, such as ' th is person' , may be viewed as abbreviat ions for descript ions invo lv ing 'he h i m s e l f and 'now ' , such as ' the person at such and such relat ive locat ion f r o m he himsel f now' . Th i s is the approach we adopt in developing our account. W h i l e i t is d i f f icu l t to deny tha t one may ignore what t ime it is or where one is, one may be more skeptical about the possib i l i ty of ignor ing who one is. I t may be argued t ha t one needs not have any object ive way of referr ing to oneself in order to know who one is. Bu t Morgenstern [1987] extends Moore's account to more general actions and plans involving several agents. She gives a consistent account of belief as a syntactic predicate, which results in a more complex but more expressive language. Selfreferential beliefs are expressible, which gives rises to paradoxical statements such as "This sentence is known to be false". But these extensions seem largely orthogonal to the issues that concern us here. Failure to appreciate this has also lead to the neglect of indexical knowledge in AI theories of knowledge and belief. ' It is possible to take 'here' as a primit ive instead and define 'he h imsel f as 'the agent located here now'. We prefer the first alternative because it seems more natural to take beliefs to be properties of agent-states rather than locations where an agent is and times. the subject ive sense of knowing-who in which th is may be the case seems qui te d ist inct f rom tha t appealed to in the par ty example and commonly explained in terms of knowing a s tandard name. Imagine an agent whose only knowledge was a l ist associating each person, represented by a standard name, w i t h his salary. W o u l d such an agent know how much he himself was mak ing? I t does not seem so. Or p u t t i n g i t another way, i f one were to c la im against common in tu i t i on tha t 'onesel f is a s tandard name, wou ld i t be leg i t imate to expect tha t al l other coreferential s tandard names wou ld be known to be coreferential? In developing our theory, we w i l l adopt an in te rpre ta t ion of knowing-who and de re belief t ha t requires the object to be known under an appropr iate objective descr ip t ion. 6 There has been disagreement among philosophers on the adequacy of s tandard possible-world semantics to handle de se a t t i tudes. Our analysis of these issues has lead us to conclude tha t whi le standard possible-world semantics is able to dist inguish between de se and nonde se bel ief (as argued by Stalnaker [ l 9 8 l ] ) , it fai ls to characterize the purely in ternal aspects of a belief state — what two agents have in common when the wor ld appears the same when viewed f rom their d is t inct perspective. Since it is these internal aspects of belief states tha t play a causal role in determin ing act ion, a semantics which provides such a character izat ion wou ld def in i te ly be super ior. In the next sect ion, we propose a logic t ha t handles de se knowledge and belief together w i t h a semantics t ha t characterizes the act ion-determin ing in ternal aspects of beliefstat.es. We take the belief accessibil ity re la t ion B to ho ld over bel ief indices, which are wor ld-agentt ime tr ip les. if wor ld w' is compat i ble w i t h what agent a believes at t ime t in wor ld w if he assumes t ha t he is a' and the current t ime is t'. Thus , the belief state of an agent at a t ime in a wor ld is m o d eled by a set of belief indices, each of which contains an agent tha t he th inks he migh t be, a t ime tha t he th inks m igh t be current , and a way the wor ld m igh t be if he is tha t agent at t ha t t ime . A belief index characterizes bo th a wor ld and the perspective f r om which i t is v iewed. Th is t rea tment of de se belief was inspired by in fo rma l proposals by Perry [ l979] and especially Lewis [1979]. The logic includes tempora l operators tha t al low one to assert tha t a state of affairs holds at a given t ime in stant ( th is was imp l i c i t in the discussion of bel ief) and tha t an agent does an act ion f rom one instant to another (adapted f r om [Reseller and Urquhar t , 1971]). B u t any character izat ion of the ab i l i ty of agents to achieve goals by do ing actions requires considerat ion of possible Our appeal to the standard name account of knowingwho in the above argument should not be taken to imply unreserved acceptance of the account or necessary dependence of our theory upon i t . 7 See [Lesperance, 1989] for a more detailed discussion of these issues. The indexicality of belief discussed here is a very distinct phenomenon from the self-referentiality allowed by Morgenstern [1987]. We are not aware of any account that would reduce the former to the latter.