Side-effects and
Cohen and Levesque's Theory of Intention
as a persistent Goal⁽¹⁾

1. Introduction

In their very interesting paper [4], Cohen and Levesque make an attempt to characterize the "rational balance needed among the beliefs, goals, plans, intentions, commitments, and actions of an autonomous agent." Such an effort is seen as a contribution to Artificial intelligence research in that [4] provides "constraints on the design of an autonomous agent." As a step in that direction, [4] presents an analysis of intention as "a kind of persistent goal" and remarks that, to the extent that such an analysis captures our ordinary concept of intention, it can be seen as a contribution to the philosophy of mind.

C&L's⁽²⁾

theory of intention is designed to meet a number of desiderata which are gathered from either the philosophical (cf. Bratman [1]) or the A.I. (cf. McDermott [6]) literature on the topic. Prominent among such desiderata is the following:

(7) Agents need not intend all the expected side effects of their intentions.⁽³⁾

C&L point out⁽⁴⁾ that many theories of intention fail to meet (7) and rightly devote a meticulous attention to it. As a matter of fact. C&L succeed in providing a theory in which 7 is met, provided certain conditions are satisfied.

I will show however that our ordinary concept of intention may require that 7 is met even in cases in which these conditions are not satisfied. In other words ,C&L's analysis , as an analysis of our ordinary concept of intention, is not fully succesful.

If - as it seems reasonable - a satisfactory account of intention is a central issue in the design of an autonomous agent, we have a problem not only for Cohens and Levesque's theory qua contribution to the philosophy of mind, but also to it qua contribution to artificial intelligence. I will then give some indications for a different treatment - based on Castanedas [3] proposition/practition distinction - which indeed meets desideratum (7).

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2. The problem of side effects

We shall say that q is a side effect of p with respect to a given context such as a legal/moral code or a system of intentions, if the context in question warrants the acceptance of p, and, on the other hand, p implies, in some relevant sense, q.

That side effects can constitute a problem can be illustrated by the following version of a paradox usually referred to - for reasons that will appear clear in a moment - as the good Samaritan paradox.⁽⁵⁾

This paradox arises once one grants (D1) below, which, on the face of it, appears at a first glance quite reasonable.

(D1) (X performs A implies X performs B) implies (O (X performs A) implies O(X performs B)) (where "O" stands for "it is morally obligatory that . . ." , here 'X performs B plays the role of a side effect of 'X performs A , with respect to "the moral code")

Now, suppose that John will murder Tom in a week and that today he wounds him by accidentally running over him with his car. We can thus assume that the following is true:

(1) O (John who is the man who will murder Tom in a week takes Tom to the hospital)

(2) John who is the man who will murder Tom in a week takes Tom to the hospital implies John will murder Tom in a week.

Now, from (D1) , (1) and (2) , it follows immediately that

(3) O(John will murder Tom in a week)

and yet one can take as an obvious datum that

(4) it is not the case that O (John will murder Tom in a week).

The obvious correlate of (D1) for a theory of belief and intention is the following:

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(I1) ((X intends to A) & (X believes that A implies B)) implies (X intends to B) (where X ranges over rational agents, here B plays the role of a side effect of A, with respect to Xs system of intentions, relative to Xs beliefs).

As in naive deontic logic, (I1) leads to an analogue of the good Samaritan paradox, once some quite reasonable empirical data are granted. Consider, for instance, the following story adapted for the purposes of this paper from Castaneda [3] , ch. 6, sect.3, p. 167.

Corliss is affected by lycanthropy and knows that tomorrow night - there will be a full moon - he will quite unintentionally scare his friend Marco who is visiting him for a few days. He then frames a certain intention, which we can report as follows:

(5) Corliss intends to apologize to Marco before scaring him (during the lycanthropy attack).

We can assume that Corliss is rational enough for the following to be true:

(6) Corliss believes that to apologize to Marco before scaring him (during the lycanthropy attack) implies scaring Marco.

But then, by (I1) , (5) and (6) it follows that

(7) Corliss intends to scare Marco.

On the other hand, Corliss lycanthropy attack, from which his scaring Marco ensues, does not depend on Marcos will. Accordingly, it is fair to admit that

(8) Corliss does not intend to scare Marco.

If one does not want to tamper with basic laws of logic, it appears that (I1) , though prima facie quite reasonable, needs some rethinking. And in fact Cohen and Levesque have chosen to formalize intention in such a way that (I1) does not always hold. To illustrate how they have achieved this will be the main goal of the next section.

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3. An overview of Cohen and Levesque's framework

C&L adopt a first order language - call it L - with two kinds of restricted variables , agent variables ranging over agents , and action variables ranging over sequences of events. In addition to standard connectives, quantifiers and uninterpreted predicates , L includes a number of special symbols. The grammar for the relevant ones is as follows (where the arrow abbreviates "is a" ):

(HAPPENS <action expr> ) R <wff> intuitively, "HAPPENS a" means that a is the next action to occur;

(DONE <action expr>) R <wff> intuitively, "DONE a" means that a has just occurred;

(BEL <agent expression> <wff>) R <wff> intuitively, this means that the proposition expressed by <wff> follows from the beliefs of the agent denoted by <agent expression>;

(GOAL <agent expression> <wff>) R <wff> intuitively, this means that the proposition expressed by <wff> follows from the beliefs of the agent denoted by <agent expression>;

<action expression> ; <action expression> R <action expression>

intuitively, the action denoted by the leftmost action expression immediately precedes, in a temporal sense, the rightmost one;

<wff>? R <action expression> intuitively, "?" corresponds to the English "to bring about" as prefixed to an English sentence.

As can be seen then, action variables are not the only kind of action expressions (though they are the only primitive ones.) On the contrary, C&L have chosen to simplify matters by having agent variables as the only "official" kind of agent expressions. Agent constants are used only unofficially.

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C&L do not provide an axiomatic or proof-theoretic characterization of L. They provide instead a possible world semantics whose main features are sketched below.

A model M for L is an 8-tuple <J,P,E,Agt,T,B,G,J>

where is a set of things , P a set ot people, E a set of primitive event types, Agt a function from E into P, T a set of courses of events (worlds) represented as functions from the integers into E, B and G are, respectively, the belief and goal accessibility relations , J is a traditional interpretation function for predicates except that it is relativized to a world and to an integer which functions as an event index.

The reader should keep in mind that C&L simplify matters by purposely neglecting the obvious fact that more than one event can take place over the same time interval. This is why worlds are modelled as courses (i.e. sequences) of events. Action expressions, in turn, are seen as denoting sequences of events which involve exactly one agent.

Here follows the interpretation of the special symbols that will be relevant to the ensuing discussion. For "A" ranging over wffs, "a" and "b" over action expressions and "s" and "s'" over sequences of events, n an integer, v a set of bindings of variables, we have:

6. M,s,v,n Ć (Agt x a) iff Agt(v(a)) = v(x)⁽⁶⁾

8. M,s,v,n Ć (BEL x A) iff for all s, such that s is accessible via B_v(X), M,s',v,n A;

9. M,s,v,n Ć (GOAL x A) iff for all s, such that s is accessible via G_v(X), M,s',v,n A;

10. M,s,v,n Ć (HAPPENS a) iff for some m ł n, M,s,v,n[a]m

11. M,s,v,n Ć (DONE a) iff for some m Ł n, M,s,v,n[a]m

"[...]" stands for a relation mutually recursive with Ć and such that:

event variables: M,s,v,n[a]n+m iff v(a) = e₁...e_m and s(n + i) = e₁, 1 Ł i Ł m (that is, intuitively, M,s,v,n[a]n+m iff a denotes a sequence of events of length m which appears next after n in the world s);

Sequential action: M,s,v,n[a;b]m iff for some n Ł k Ł m, M,s,v,n[a]k and M,s,v,k[b]m;

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Test actions: M,s,v,n[A?]n iff M,s,v,n Ć A.

The definitions of satisfiability and validity are standard. Note, however, that C&L's models contain neither a designated member of T, representing the actual world, nor a designated integer, representing the present moment of time, hence, the notion of truth must be relativized not only to a model M, but to a world s and to an integer n.

The accessibility relation B for belief is serial, transitive and Euclidean. the accessibility relation G for goals is serial. This means that C&L's logic of goals corresponds to a weak T modal logic, whereas their logic for beliefs corresponds to weak S5 modal logic.

In other words, the following propositions hold in C&L's system:

Proposition 10 Belief axioms:

a) Ć (BEL x p) & (BEL x (p q)) R (BEL x q)

b) Ć (BEL x p) R (BEL x (BEL x p))

c) Ć -(BEL x p) R (BEL x -(BEL x p)

d) Ć -(BEL x false)⁽⁷⁾
 
 

Proposition 11

If Ć A then Ć (BEL x A)

Proposition 16

Ć -(GOAL x false)

Proposition 17

Ć ((GOAL x p) & (GOAL x (p R q) ) ) (GOAL x q)

Proposition 18

if Ć A then Ć (GOAL x A) .

Furthermore, the following most important propositions relating GOAL and BEL hold as well:

Proposition 19

Ć (BEL x p) R (GOAL x p)

Proposition 21 expected consequences

Ć ( (GOAL x p) & (BEL x (p R q)) R (GOAL x q).

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As regards belief, it is well known that propositions 10-11 (reminiscient of Hintikka [5] ) constitute too strong a characterization of belief, in the sense that at best they have to do with the beliefs of an ideal logical agent who never believes contradictions, and has an infinite number of beliefs (she believes whatever follows logically from her beliefs and moreover believes that she believes whatever she believes).⁽⁸⁾

Alternatively, propositions 11-12 can be seen as characterizing what is implicit in (i.e. follows logically from) the explicit beliefs of an ordinary agent who happens to have no contradictory explicit beliefs.

Analogously, GOAL characterizes what is implicit in (i.e. follows logically from) what an agent has explicitly chosen as a goal, plus whatever she implicitly believes. It is assumed that agents never choose contradictory goals.

In sum, our understanding of C&L's predicates "BEL" and "GOAL" presupposes an understanding of two very basic notions which C&L do not fully take into consideration, let alone formalize: to believe (something) explicitly, and explicitly choosing (something) as a goal.

While I think that an intuitive grasp of what it is to believe something explicitly may be sufficient for C&L s purposes, things are not so smooth as regards goals. It is not obvious in fact how to explicitly choose something as a goal differs from intending something. But GOAL, as we shall see, is a primitive that C&L use in their analysis of intending. There is, in other words, an air of circularity, but for the purposes of this paper we can assume that the issue can be satisfactorily clarified.

At any rate, it is important to note that it is empirically possible that, for some x and p, "(BEL x p)" and "x explicitly believes p" are simultaneously true. Something analogous should hold for GOAL and its "explicit counterpart," whatever that exacty means. It is important to keep this in mind, for it means that the discussion in sect. 3 will stand even if "BEL" and "GOAL" are interpreted so as to catch the notion of explicitly believing and choosing as a goal.

I move now to a number of definitions that are relevant in order to understand C&L's notion of a persistent goal and hence their analysis of intention:

EVENTUALLY: ŕ A =df $x(HAPPENS x;A?) intuitively, A is true at some point in the future

ALWAYS: r A =df "x((HAPPENS x) R (HAPPENS x,A?))

intuitively, A is true throughout the course of events

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Definition 1 (DONE x a) =df (DONE a) & (Agt x a)

intuitively, x is the agent of the action a which has just been realized

Definition 2 (HAPPENS x a) =df (HAPPENS a) & (Agt x a)

intuitively, x is the agent of the action a which is going to happen next

Definition 3 (LATER p) =df -p & ŕ p

intuitively, p is not presently true, but will be true at some point in the future

Definition 4 (BEFORE p q) =df  "c((HAPPENS c,q?) R $a((a Ł c) & (HAPPENS a;p?)))

intuitively, p comes (temporally) before q, in the sense that, whenever q is true in a course of events, p has been true in that course of events⁽⁹⁾
 
 

We finally come to the notion of persistent goal:

Definition 8 (P-GOAL x p) =df (GOAL x (LATER p)) & (BEL x -p) & (BEFORE ((BEL x p) (BEL x r -p)) -(GOAL x (LATER p)))

"(P-GOAL x p)" could be read as "x has p as a persistent goal," and, intuitively, is defined as "x has p as a goal that he will not give up until he thinks it has been satisfied, or until he thinks it will never be true"⁽¹⁰⁾.

Now, it is important to keep in mind that the following propositions do not hold in C&L's framework:

case 2 Ć (((P-GOAL x p) & (BEL x (p R q)) R (P-GOAL x q))

case 3 Ć (((P-GOAL x p) & (BEL x r (p R q)) R (P-GOAL x q))

case 4 Ć (((P-GOAL x p) & r (BEL x r (p R q)) R (P-GOAL x q))

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However, C&L implicitly inform us that these conditionals hold under special circumstances:

Case 2 fails because that implication [p R q] cannot affect the agents persistent goals, which refer to ps being true later. That is, the agent believes p is false and does not have the goal of its currently being true.

Consider case 3, where the agent believes the implication always holds. Although proposition 19 tells us that the agent has q as a goal, we show that the agent does not have q as a persistent goal ... If the belief changes, the agent need no longer choose worlds in which p R q holds, and thus need no longer have q as the goal.

Now, consider case 4, in which the agent always believes the implication. Again, q need not be a persistent goal, but for a different reason. Here the agent could believe the side-effect already held. Hence, by the second clause in the definition of P-GOAL, the agent would not have [q as] a persistent goal. (cf. C&L [4] p. 324.)

Let us concentrate, for simplicity, just on case 4. On the basis of the quotation above, we can assume (see however proof in the appendix) that the following holds:

Proposition 100 (where we drop for readibility the prefix "M,s,v,n Ć")

If

(a) (P-GOAL x p)

(b) r (BEL x r (p R q))

(b) (BEL x -q)

(d) r -(BEL x r -p),

then

(e) (P-GOAL x q)

Proposition 100's premise (d) cannot be explicitly gathered from C&L's quotation. However, it must be added to insure that the agent does not drop p from her goals because she comes to believe that p will never be true. Of course, if the agent drops p to begin with, we have no ground to attribute to her the side effect q as a persistent goal.

We finally come to C&L's characterization of intending, which will be central to the ensuing discussion. To be more precise, C&L distinguish two different notions of intending, which they label "INTEND₁"and "INTEND₂" respectively. "INTEND₁" takes action expressions as arguments, whereas "INTEND₂" takes expressions for states of affairs (propositions or, in general, entities expressed by wff's).

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According to C&L, "INTEND₂" has to do with those cases in which an agent intends (to bring about) a certain state of affairs without having (at the time in which she frames the intention) a clear idea of how to proceed in order to realize the intention. I shall not dwell on "INTEND₂", though I believe that most of what I will say below about "INTEND₁" applies, mutatis mutandis, to "INTEND₂" as well.

C&L's definition of "INTEND ₁" is the following:

Definition 10 (INTEND₁ x a) =df (P-GOAL x (DONE x (BEL x (HAPPENS a))?;a))

where a is an action expression

(Since I will not be dealing with INTEND₂ any longer, I shall drop for simplicity the subscript "1" from "INTEND₁".)

Intentions are thus, in C&L's analysis, rather peculiar kinds of persistent goals. Hence, from proposition 100 and definition 19 above, it follows that:

Proposition 200 (again the prefix "M,s,v,n Ć" is neglected)

If

(a') (INTEND x a)

[that is, if

(a'') (P-GOAL x (DONE x (BEL x (HAPPENS a))?;a))]

(b') r BEL(x r (DONE x (BEL x (HAPPENS a))?;a) R (DONE x (BEL x (HAPPENS b))?;b)

(c') BEL(x -(DONE x (BEL x (HAPPENS b))?;b))

(d') r -BEL(x r -(DONE x (BEL x (HAPPENS a))?;a)),

then

(e') P-GOAL(x (DONE x (BEL x (HAPPENS b))?;b))

[that is,

(e'') (INTEND x b)]

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In the next section, we shall see that Corlisss story allows us to instantiate the variables of Proposition 200 in an empirically plausible way, thereby suggesting to us that desideratum (7) is not fully met by C&L's framework.

4. Corliss story and intention as a persistent goal

Assume for convenience the following abbreviations:

Abr1) a =df to apologize to Marco before scaring him (during the lycanthropy attack)

Abr2) b =df scaring Marco

Abr3) A =df (DONE Corliss (BEL Corliss (HAPPENS a))?;a)

In English: Corliss has just brought about that Corliss believes a is about to happen and immediately after a happens.

Abr4) B =df (DONE Corliss (BEL Corliss (HAPPENS b))?,b)

In English: Corliss has just brought about that Corliss believes b is about to happen and immediately after b happens

Now, in the context of Corliss story, it is true that

(A) (INTEND Corliss a)

and

(A') -(INTEND Corliss b).

Nevertheless, in view of proposition 200,

(E) (INTEND Corliss b)

follows from

(B) r BEL(Corliss, r (A R B))

(C) BEL(Corliss, -B)

(D) r -BEL(Corliss, r -B).

Let us take (B) , Š and (D) in turn. (B) says that at all times Corliss will believe that at all times Corliss belief that a is about to occur immediately followed by as occurrence implies Corliss belief that b is about to occur immediately followed by bs occurrence. Since intuitively a's occurrence

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implies b's occurrence, in endorsing (B) all we are doing is in effect to attribute to Corliss, so to speak, some amount of rationality coupled with certain beliefs about this rationality.

The first occurrence of the temporal operator "r" in (B) deserves some comment, for it seems to imply that Corliss is eternal. This seems a bit unrealistic, though C&L say they have assumed "immortal agents".⁽¹¹⁾ This is of course an idealization that simplifies matters. However, for present purposes, note that the strong premise (B) can be substituted by a weaker one that simply insures that Corliss believes that r (A R B) at all times in which this is needed in order to reach the desired conclusion (see case 3 in the quotation above from C&L [4]).

As far as (C) is concerned, obviously, when Corliss frames his intention he does not believe that his believing he is about to scare Marco, followed by Marcos being scared, is true yet. Hence, (C) can safely be assumed.

Finally, (D) says that Corliss never believes that his believing he is about to scare Marco, actually followed by his scaring Marco, will never take place. This is possible if Corliss feels sure of his having the lycanthropy attack and of the effects of his attack on Marco. Obviously there is nothing wrong with that.

In conclusion, it is perfectly possible to complement Corliss story with (B), (C) and (D), thereby deriving the undesired conclusion that Corliss intends to scare his friend Marco.

To fully see the relevance of Corliss story to A.I. research, imagine a robot designed in accord with C&L's theory and which is programmed to assist Corliss to bring about his intentions and to forestall what runs against them. Obviously this robot will act on the basis of his understanding of Corliss beliefs and intentions. Suppose the robot is smart enough to understand Corliss intention to do a and to understand that (B), (C) and (D) hold. Then the robot will wrongly attribute to Corliss the intention to scare Marco and will do nothing to prevent this from happening.

5. Intentions and the practition/proposition distinction

Castaneda originally developed the practition/proposition distinction in order to deal with the paradoxes of deontic logic, one of which was presented in sect. 2. In Castaneda [3] this distinction is also used toward the development of a theory of intentions.

Roughly, propositions are entities which are true or false and which are typically expressed by sentences in the indicative mood, practitions instead have no truth value, though they can be "designated" in the sense that they can be endorsed by, say, a legal or moral code or by a system of intentions. Practitions can be expressed by sort of infinitive expressions and typically, for every proposition, there is a corresponding practition. So, for example, to the

proposition expressed by "Mary is turning off the light", there corresponds the practition "Mary to turn off the light."

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According to Castaneda [3]. connectives and quantifiers can be used to generate complex practitions from simple (atomic) ones much as they can generate complex propositions. In addition, connectives can combine practitions and propositions together, with the proviso that any such mixed combination counts as a practition.

Furthermore, according to Castaneda [3], intending takes always a practition and never a proposition as its second argument.

For purposes of illustration, consider a simple first order language which is augmented as follows:

1) If A is an atomic wff, (A)* is an atomic p-wff

where the "p-" prefix reminds us that we are now dealing with a practition

2) If x is any variable, A a wff, and P and Q are p-wffs, -P, (P & Q), (A & P) and "x(P) are p-wffs.

3) If a is a singular term, A a wff and P a p-wff, (BEL a A) and (INTEND a P) are all wffs.

Let us now consider the counterpart of (I1) in such a language:

(I1) ((INTEND X P) & (BEL x ((INTEND x P) R (INTEND x Q))) R (INTEND x Q)

where P and q are p-wffs

Now, whatever proof/model-theoretic content is given to the above simple language, the idea is that (I1) should count as valid in order to preserve the intuition that there is something right after all in (I1).⁽¹²⁾

To see however that a full acceptance of (I1) does not run against desideratum (7), consider Corlisss story again.

Since for simplicity our simple language does not include temporal modalities, let us modify the story slightly: now Corliss intention is not to apologize to Marco before he scares him, but rather while it is the case that he scares him. We can understand this "while" as expressing a conjunction. Of course, this simplification is uninfluential for the generality of the point being made. Let us use the abbreviations below, which are suggestive of how Corliss story should be formalized according to the practition/proposition theory:

Abr1') P =df (the practition) Corliss to apologize to Marco (where P is a p-wff)

Abr2') A =df (the proposition that) Corliss scares Marco (where A is a wff).

Now we can certainly assume that

1) (INTEND Corliss (P & A))

and

2) (P & A) R A.

Furthermore, we can assume that Corliss is rational with respect to 2), which we can express as follows:

3) (INTEND Corliss P & A) R (BEL Corliss A).

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The basic idea behind this analysis of Corliss story is that what Corliss actually sees as something he intends to bring about of his own will is read as a p-wff expressing a practition, whereas what he sees as a circumstance "surrounding" his intentions and which has a truth value independently of them is read as a wff expressing a proposition or state of affairs (which he believes to be true).

Now we cannot use (I1') in order to derive

4) (INTEND Corliss A).

The reason is that 4), as well as

5) ((INTEND Corliss (P & A)) & (BEL Corliss ((INTEND Corliss (P & A)) R (INTEND Corliss A))) R (INTEND Corliss A) (where P and q are p-wffs)

are not wffs, since A is not a p-wff expressing a practition, and hence cannot be the second argument of "INTEND."

Of course, all I have presented here is just a sketch, not a fully developed formal theory. Nevertheless, we have precise enough indications to work out a formal theory of intention which fully meets desideratum (7). The development of such a theory must be the object of future work.

APPENDIX I

Proposition 100 (where we drop for readibility the prefix "M,s,v,n Ć")

If

(a) (P-GOAL x p)

(b) r (BEL x r (p R q))

(c) (BEL x -q)

(d) r -(BEL x r -p)),

then

(e) (P-GOAL x q).

Sketch of proof.

Note first that by definition 8 of "P-GOAL", we need to prove, given the premises, the following three conclusions:

(1) (BEL x -q)

(2) (GOAL x (LATER q))

(3) BEFORE[((BEL x q) Ú (BEL x r -q)) -GOAL(x LATER q).

Conclusion (1) is already among the premises. As regards (2) and (3),I shall freely use facts 0-2 below:

Fact 0 BEL works like a necessity operator in a weak S5 modal logic

Fact 1 GOAL works like a necessity operator in a weak T modal logic

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Fact 2 If M,s,v,n, Ć B and, for each A₁ (1 Ł i Ł m), either Ć A₁ or at least M,s,v,n Ć r A₁, then

(i) Ć A₁ & ... & A_m & B C and

(ii) M,s,v,n Ć (HAPPENS x,B?) imply M,s,v,n Ć (HAPPENS x,C?).

This is so because, in virtue of the semantics of "HAPPENS", sequential action and test action, the context "(HAPPENS x; ... ?)" essentially just causes a "time shift" for the evaluation of any formula A. But obviously any formula which is logically valid or at least valid at all times, will be valid also at the time to which the evaluation of A is "shifted."

Let us now concentrate on (2). We need to prove, in view of definition 3, that

(4) (GOAL x (-q & ŕ  q)).

Given (c), proposition 19 and fact 1, it is enough to show

(5) (GOAL x ŕ q).

We shall proceed as follows:

(6) (GOAL x (HAPPENS y;p?))

from (a) by definition 8, conjunction elimination, fact 1, definition 3, EVENTUALLY, conjunction elimination and existential instantiation

(7) (GOAL x r (p R q))

from (b) by proposition 19, fact 1, ALWAYS, and truth conditions on sequential actions, test actions and "HAPPENS"

(8) (GOAL x (HAPPENS y;q?))

from (6) and (7) by facts 0-2

The desired result now follows immediately by existential generalization (',within" GOAL, in virtue of fact 1 and EVENTUALLY.

Let us now turn to (3). In what follows, I shall adopt the following abbreviations:

Abr3) A =df (BEL x q) Ú (BEL x r -q)

Abr4) B =df -(GOAL x (LATER q))

By definition 4, all we need to do is to assume

(9) (HAPPENS c;B?) for a generic c

and show

(10) $a(a Ł   c & (HAPPENS a;A?)).

We approach the desired conclusion as follows:

(11) (HAPPENS c;(-(GOAL x (LATER p)) Ú -(BEL x ((LATER p) R (LATER q)))?)

from (9), by proposition 21 and fact 2, using contraposition

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(12) (HAPPENS c;-(GOAL x (LATER p))?)

from (11) and (b), by proposition 19, facts 0 and 2, definition 3 and disjunction elimination

(13) $a(a Ł c & (HAPPENS a; ((BEL x p) Ú (BEL x r -p))?))

from (a), definition 8, definition 4, universal instantiation, (12) and modus ponens

(14) a Ł c & (HAPPENS a; (BEL x p)?)

from (13) by existential instantiation and (d) by fact 2 and disjunction elimination

(15) a Ł c & (HAPPENS a; (BEL x q)?)

from (14) and (b) , by facts 0 and 2

(16) a Ł c & (HAPPENS a; ((BEL x q) Ú (BEL x r -q))?)

from (15) by fact 2 and disjunction introduction)

(17) (13) from (16) by existential generalization

Q.E.D.

Appendix II

Throughout the course of this paper I have simplified matters by neglecting the most important issue of quasi-indicators.⁽¹³⁾

Typically, reports about other peoples beliefs and intentions go like these:

(A1) The tallest man believes that he is rich

(A2) Marta intends to kill herself.

Here "he" and "herself" are, in Castaneda [2]s terminology, quasi-indicators, that is, pronouns used within the scope of a mental attitude verb and which refer back to a noun phrase which

(i) lies outside the context of this verb and

(ii) refers to the subject of the mental attitude.

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Quasi-indicators are used to express the self- reference that a person other than the speaker would express by means (in English) of the pronoun "I."

(A1) and (A2) are not equivalent, respectively, to

(A1^*) the tallest man believes that the tallest man is rich

and

(A2^*) Marta intends to kill Marta.

For example, if the tallest man does not believe to be the tallest man, (A1^*), under a certain reading, may have a truth value different from (A1).

C&L's framework does not encompass agent constants or definite descriptions. However, if it were augmented so as to include them, and C&L's analysis of intention remained the same, quasi-indicators would create a problem. For example, plug in "the tallest man" and "to go to Milan" for "x" and "a," respectively, in definition 10. Then, intuitively, the left side of Definition 10 could be true, and the right side false for the tallest man might intend to go to Milan, but fail to believe that he is the tallest man.

For the importance of quasi-indicators in A.I. research, see Rapaport [7].

BIBLIOGRAPHY

[1] Bratman. M.: Intentions, Plans, and Practical Reason. In preparation.

[2] Castaneda, H.-N.: "Indicators and Quasi-indicators", American philosophical Quarterly 12(1967) : 131-40.

[3] Castaneda, H.-N.: Thinking and Doing, Reidel, Dordrecht, Holland, 1975

[4] Cohen, P.R., Levesque, H.J.:

"Persistence, Intention, and Commitment." in M. Georgeff and A. Lansky (eds.), Reasoning about Actions and Plans, Morgan Kaufman 1987.

[5] Hintikka, J.: Knowledge and Belief - Cornell University Press, 1962.

[6] McDermott, D.: "A temporal logic for reasoning about processes and plans." in Cognitive Science 6 (1982) : 101-55.

[7] Rapaport, W.: "Logical Foundations for Belief Representation," in Cognitive Science 10(1986) : 371 - 422.

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NOTES

1. A formal characterization of intention is an important step

toward the design of an autonomous agent. This paper provides an

overview of Cohens and Levesque's [4] formalization of intention as a persistent

goal within a possible world framework. C&L s theory is then criticized for its failure to fully meet the desideratum that agents need not intend all the expected side-effects of their intentions. Finally, it is proposed that Castanedas[2] proposition{practition distinction provides a way to meet this desideratum.

2. "C&L" abbreviates "Cohen and Levesque." Any reference to C&L is really a reference to their work C&L [4].

3. Cf. C&L [4], p. 302

4. note 7, p. 302

5. For some bibliography regarding the Good Samaritan paradox see Castaneda [3] note 7, p. 236.

6. As far as I can see. it is not clear from C&L [4] how "Agt" is interpreted when a is not a variable. However, this will be uninfuential for what follows.

7. "false" is a wff that is always false. So, proposition 10 d) means that x never believes contradictions.

8. Incidentally" C&L's agents are "ideal" in other respects as well. Consider for example C&L's definition of an agent being competent about a proposition p:

Definition 16 (COMPETENT x p) =df (BEL x p) R (KNOW x p)

where "(KNOW x p)" is defined as "(BEL x p) & p".

Since a conditional with a false antecedent is always true, it is enough that -(BEL x p) for (COMPETENT x p) to be true. That is, paradoxically enough, agents are competent at least about everything that they do not believe !

The notion of competence, at any rate, has a relatively minor role in C&L's framework, hence I shall not pursue this any further.

9. C&L do not explicitly introduce the symbol " Ł  ". However, since events are correlated with integers, it is obvious what the interpretation of " Ł  " should be.

10. Cf. C&L [4] p. 322

11. Cf. note 18, p. 320

12. Provided of course that we are dealing with rational agents.

13. Cf. Castaneda [2]

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