The change of beliefs on the basis of new information has been widely studied; however, the change of other mental states has received less attention, and particularly, intentions. Despite there are philosophical and formal theories about intentions, few of them consider the revision of intentions.We suggest introductory guidelines to de ne a research program for the revision of intentions regarding that: (i) intentions are intimately related to the beliefs and desires of agents immersed in a dynamic world; (ii) intentions are directly related to planning; and (iii) a reconsideration function is needed.
Belief revision is a paradigmatic research program: it is a relatively new area
of research that joins two diciplines: computer science and philosophy. Since
programmers dealt with databases they faced the problem of updating their
information. On the other hand, certain philosophers dealt with the change of
information within epistemic structures. So, we can identify, respectively, two
important moments in the history of this research program: one in [
Thus, although the change of beliefs on the basis of new information has
been widely studied with success during the last 25 years, the dynamic process
of other mental states has received less attention, and particularly, intentions
[
In this work we suggest some general and introductory guidelines in order to de ne a program for intention revision. We think this topic is important because (i) intentions are intimately related to the beliefs and desires of the agents immersed in a dynamic world; (ii) intentions are related directly with planning; and (iii) a function of reconsideration is needed.
The general background of this work assumes the theories of intention as
represented by [
The rest of the paper is distributed in the next way: in section 2 we describe what do we mean by intention revision and we describe some methodological problems. In section 3 we discuss some issues regarding the problem of representation. In section 4 we adapt and suggest some general postulates for the revision of intentions. Finally, in section 5 we discuss the ideas of this introduction and we give some details about future work. 2
We can study intentions from two general perspectives. One internal, e.g., what are intentions and how do they behave; the other, external, regarding the problems intentions generate, e.g., how do they relate to other mental states and how those relations can be modelled. We will follow this double approach. 2.1
Internal perspective
For our introduction we will need an approach based upon the BDI model of
rational agency [
Intentions, as an irreducible component of the BDI model [
In this way, we can say that intentions require a notion of commitment (given the principle of pro-activity), a notion of consistency (given the admissibility criteria) and a notion of retractability (given the notion of inertia).
Plans, as long as they are sets of actions, are intentions and in this sense,
they share the same properties: they are conduct-controlling, they have inertia
and they work as inputs for future practical reasonings [
{ Internal consistency. Plans must be executable. { Strong consistency. Plans must be consistent with the agent's beliefs. { Means-ends coherence. The means-ends reasoning of the plan must be consistent with the global ends of the plan.
These last features lead us to consider some other problems: that intentions
are not isolated mental states [
Thus, we can say that the notions of consistency and retractability are not exclusive of beliefs; and that the di culty of considering intention revision lies in the relation between intentions and beliefs. 2.2
External perspective
Based on Bratman, Cohen and Levesque [
{ 4. Agents believe their intentions are possible. { 5. Agents do not believe they will not bring about their intentions. { 6. Under certain circumstances, agents believe they will bring about their intentions. { 7. Agents need not intend all the expected side e ects of their intentions.
With these criteria, Cohen and Levesque construct a formal theory of
intention based on the notion of persistent goal (according to them, an intention
is a form of persistent goal [
{ 8. Agents can retract their intentions when such intentions present problems. Broadly speaking, this idea is the one that constitutes the core of intention revision. 2.3
What is intention revision? An example
Let us see, by way of an example, what is intention revision. Assume our agent is
immerse in an environment that is inaccesible, non-determistic, episodic, discrete
and dynamic [
In this way, the agent generates an intention of the form put(B; C). Now, given the properties of the environment, let us suppose the agent perceives the state -which is denoted by the red arrow- where it is not the case that f ree(C). Therefore, the intention will fail, the set of intentions would become inconsistent and the goals of the agent will not be achieved.
Let us see this situation in a more precise way. Suppose that we have an agent with a database of intentions -and beliefs- that includes the next data: { p1 !put(x; y). { p2 +!put(x; y) : f ree(x). { p3 +!put(x; y) : f ree(y).
{ p4 +!put(x; y) : !move(x). where ! stands for an intention formula and + for an addition of a formula. If the database is equipped with some inference engine, the next formula is required to accomplish the intention:
{ p5 f ree(x).
Now, suppose that it is the case that x is not free. This means that we have to add the negation of p5 to the database. But then the set of intentions becomes inconsistent in an intuitive sense. If we want to keep the database consistent, which is a sound methodology, we need to revise the database. This implies that some of the intentions may have to be retracted; however, we do not need to revise the whole set of intentions for that would be an unnecessary lost of time and information. Thus, we have to choose what formulas -i.e., intentions- to retract.
The problem of intention revision, thus, is double: in rst place, because it is intimately related to other mental states (like beliefs and desires); and in second place, because logic by itself is not su cient to determine which intentions should be retracted. These problems lead us to take into account that the change of intentions is associated with changes in beliefs, and that we require extra-logical concepts to deal with these changes.
To complicate the setting even more, beliefs and intentions have certain logical consequences: when retracting intentions we have to choose which consequences (beliefs or intentions) we have to retract.
But to mantain the consistency and the maximum number of intentions accomplished, should we revise all the intentions? The answer is no, because, as we will see, the costs over time and memory would be huge. 2.4
Some methodological problems with intention revision
When dealing with intention revision some methodological problems appear: one
related to representation, one related to inference, and nally, one related with
a function of selection.
{ The problem of representation. How should the intentions be
represented? Most databases work with facts and rules of some kind. The
language used to represent intentions -together with beliefs and desires- may
be related to some logical formalism (for instance, rst order logic). This
problem is, therefore, double: what language should we use to represent our
data? And is this language adequate to relate the BDI components within a
context of revision?
{ The problem of the consequences. What is the relation between the
elements represented as facts and the elements that are inferred? This
relation is sensible to the database. In some cases the elements that have been
inferred have some special status in comparison with the facts; however,
depending on which representation we use we will be able to distinguish these
di erences.
{ The problem of the function of selection. How should we choose which
elements to retract? Logic by itself is not su cient to decide which intentions
should be maintained and which intentions should be retracted. We need a
heuristic to determine this selection. One idea is that the loss of information
should be minimal, for instance, by way of an ordering [
We will use a propositional model considering that the elements of the intentional system are propositional formulas. Of course, even with this representation we can have several alternatives. First, we have to pick an appropriate language (for instance, databases may be represented in a Prolog style). In this introduction we will work with a rst order language.
We assume that the language L is closed for the operators :, ^, _, ) evaluated in a boolean way. We use ; ; ::: as propositional variables in L. The language L not only accepts what is explicitly represented in the database, but also, the consequences of it. Thus, another factor we have to determine is: which logical system should govern the set of intentions? In practice, the answer to this question depends on what mechanism of inference is coupled with the database; however, when doing this theoretical analysis, we will proceed by declaring the general functions of revision. So, for this introduction, we will use a classical propositional logic. 3.1
Sets of intentional states The easiest way to represent an intentional state is by using well-formed formulas (w ) of L. According to this, we can de ne a set of intentional states (intentional set, from now on) through a set of w of L that satisfy the axiom of generalized re exivity (C): if ` then 2 . The condition C assures us that is closed under logical consequence. By the properties of classical logic, whenever is inconsistent, then for all , ` . We will denote this with ?. This means that there is an intentional set that is inconsistent.
There is a very close correspondence between intentional sets and possible worlds models. For any set W of possible worlds we can de ne a corresponding intentional set as the set of those sentences that are true in all worlds in W . From a computational point of view, however, intentional sets are much more tractable than possible worlds models. 3.2
Intentional bases Nevertheless, we have to consider that some intentions are not basic, but inferred. It is not possible to express this distinction through intentional sets, for the set theoretic representation does not provide markers or ags to indicate which intentions are basic and which are inferred. Moreover, it seems that when we make intentional changes we do not change the whole set of intentions, but a nite subset of it. Formally, this idea can be represented by letting B be a base for an intentional set if and only if B is a nite subset of and Cn(B ) = . Then, we introduce the functions for intention revision in bases of intentions (intentional bases from now on). The distinction between intentional set and intentional base allows us to generate and distinguish di erent structures, e.g., assume two intentional bases B and B0 such that Cn(B ) = Cn(B0 ) but B 6= B0 . If we want to implement intentional revision systems, intentional bases are easier to handle than intentional sets. 4
When dealing with intention revision there are two main strategies that may be followed: to present in an explicit manner the construction of the process of revision or to formulate the general ideas to realize such constructions. The rst solution to the problem consists in developing algorithms that compute the functions; the second approach consists in describing the postulates to de ne the functions to further develop the algorithms.
In this introduction we will follow the second approach. The formulations of the postulates will be given through a series of ideas and conditions. The heuristic behind is similar to the idea of belief revision: the intentional changes should provide (i) a maximum of preservation of information (i.e., a minimum change in the intentions) and (ii) consistency.
Intention revision should occur when a new piece of information that is inconsistent with the database is added to the system in such a way that the resulting set in inconsistent. But this change is not the only one that may occur. Depending on how intentions are represented and what intentions are accepted, di erent intentional changes are possible. We can distinguish four intentional changes, three of them similar to belief changes: { Expansion. A new formula is added to a together with the logical consequences of the addition. The system that results from expanding by a sentence will be denoted as . { Revision. A new formula that is inconsistent with is added, but in order to mantain consistency in the resulting system, some of the old formulas in have to be deleted. This is denoted by . { Contraction. Some formula in is retracted without adding any new facts. In order to mantain the system closed under logical consequence, some members of must be deleted. This will be denoted by . { Reconsideration. A new formula is added to , but eventually such formula has be to contracted or revised. This is denoted by .
Expansions are closed under logical consequence (i.e., the expansion of the intentional set with a new formula is = f j [ ` g); however, it is not possible to give a similar characterization of the other changes. The problem of revision, contraction and reconsideration has its roots in the lack of purely logical reasons to accomplish these processes. Thus, we can have di erent ways to research, specify and verify them.
For the time being, we will assume that the intentional sets model intentional
bases. In what follows we will formulate some postulates for intention revision.
The motivation behind these postulates (adapted from [
Postulates for revision For intention revision, the rst postulate requires closure:
intentional set. and any intentional set The second postulate guarantees that the input sentence is accepted in the revision: Postulate 2 ( 2) 2
A revision process should occur when the input contradicts what is already in , that is : 2 . However, in order to have the revision function de ned for all inputs, we can easily extend it to cover the case when : 2= . Thus, revision is identi ed with expansion: Postulate 3 ( 3)
.
Postulate 4 ( 4) If : 2= , then
The postulates ( 1) to ( 6) are the basic postulates for revision. The nal two conditions concern composite intention revisions. The idea is that, if is a revision of and is to be changed by a further formula ; such change should be made by expansions of whenever possible. The minimal change of to include both and , that is, ^ , ought to be the same as the expansion of by , so long as does not contradict the intentions in : Postulate 7 ( 7) Postulate 8 ( 8) If : 2
= When : 2= , then ( ^ ) (
) is formed from
by giving up some intentions, no new intentions , the optimization heuristic requires that nothing has to be rePostulate 11 ( 3) If = , then 2 = .
The formula to be contracted should not be a logical consequence of the intentions in : Postulate 12 ( 4) If 6` , then
From ( 1) to ( 4) it follows that if 2= , then ( ) . In other words, if we rst retract and then add again to the resulting intentional, no intentions are accepted that were not accepted in the original intentional set. The optimization heuristic demands that as many intentions as possible should be kept in . So, we need a recovery: Postulate 13 ( 5) If , then (
) 2 This postulate enables us to undo contractions, and although it is controversial, we will assume it for sake of the introduction. The sixth postulate is analogous to ( 6): Postulate 14 ( 6) If ` These postulates are the basic set of postulates for intention contraction. Again, two further postulates for contractions with respect to conjunctions will be added. The motivations for these postulates are similar to ( 7) and ( 8). ^ , then
.
=
^
.
^
The postulates above are adaptations of [
Postulate 18 ( 2) ( ) _ (
). , is an The purpose of a reconsideration is to produce a new consistent intentional set: Postulate 19 ( 3)
= K? if and only if ` : .
Postulate 20 ( 4) If ` , , then = .
This set of postulates is the basic set of postulates for reconsideration. We also have the next ideas. The reconsideration should be done by expansions whenever possible. And the minimal change of to include and should be the same as the expansion of by .
Postulate 21 ( 5) Postulate 22 ( 6) If : Postulate 23 ( 7) ^
) ^ .
We now display some results regarding intention revision, but rst, we require some de nitions: an intention is abandoned if and only if is retracted from either by a contraction or a revision. And an intention is continued if and only if 2 ( ) .
The following results are straightforward. ^ . Proposition 1 The following statements hold: { 1. If is reconsidered, then
is abandoned or continued. ) ( _ ) _ (( ) ) { 2. Inconsistency of reconsideration results from the inconsistency of intentions. { 3. Reconsidering a consistent
any intention. { 4. Successful reconsideration produces an intentional set.
? with the current intentions does not remove ? ) ( ) = = = Proof. To prove statement 1, assume is reconsidered. By 2, it follows that _ , which means is abandoned; by addition, is continued. Statement 2 follows from 3. Statement 3 results from the de nition of a continued intention. Statements 4 follows from 1.
At this point, we have presented some issues and problems of intention revision by isolating intentions from other mental states. In the next proposition we will try to relate intentions and beliefs through the reconsideration function. To see the next results, recall that it is irrational for an agent to intent and believe at the same time that it will not achieve : this is intention-belief inconsistency. To avoid this inconsistency, an agent must abandon intentions impossible to achieve. And recall that it is rational for an agent to intent and at the same time not believe that will achieve : : this is intention-belief incompletness. To accomplish this property, an agent must continue its intentions.
The following representation theorems require some auxiliar de nitions: we say an agent believes , BEL , if 2 ; and an agent has an intention to , INTEND , if ! 2 .
Proposition 2 The following statements hold: { 1. Reconsideration implies intention-belief incompletness. { 2. Reconsideration avoids intention-belief inconsistency.
` 6` ) INTEND
^ :BEL: ) INTEND ^ BEL: Proof. Assume . Furthermore, assume that INTEND is also given. We have two options: the intention is possible or impossible to achieve. For statement 1: if the intention is possible to achieve after reconsideration, then 2 ( ) , which means the agent can continue its intention. Thus, 2 . For statement 2: if the intention is impossible to achieve, then ?, which means that the reconsideration is inconsistent, but inconsistent reconsideration cannot be the case given 5.
Intuitively, this means that if an agent reconsiders, such agent is closer to rationality by following the intention-belief incompletness property, because the agent continues intentions possible to achieve. And also, the agent is far from irrationality by avoiding the intention-belief inconsistency, because after reconsideration the agent cannot have inconsistent reconsiderations, and so, the agent has to drop intentions not possible to achieve. 5
Let us sum up some of the main ideas and results of this introduction: { A) Agents can retract their intentions when such intentions present problems. { B) If an agent reconsiders an intention, such intention is abandoned or continued. { C) If an agent reconsiders, such agent is closer to rationality by following the intention-belief incompletness property and by avoiding the intention-belief inconsistency.
So, we have sketched some general and introductory guidelines for intention revision by following the theories of intention and by considering that intentions are not isolated and are related to planning. We are aware these ideas lead to more problems. Some of the open problems we do not want to let to mention are the following: { How do we relate the topic of this introduction with a non-monotonic logic? Since we can reconsider intentions, we have the possibility to relate our proposal with a non-monotonic consequence relation. Recall from section 2, for instance, that from a state we want to achieve a state through some execution of intentions, formally:
: p1; : : : ; pn
but eventually happens that some plan pi fails, which takes to intention
revision. Future work requires the treatment of this situation.
{ How do we relate the BDI components and temporal logic with the postulates
we have proposed? One of the problems that we have presented is that,
although we provide an abstract de nition of the revision functions, we do
not take into account the role of time within the reasoning process. Another
problem is that we have considered intentions in an isolated way; this is
necessary nonetheless, since intentions are irreducible componentes of the
BDI architecture [
The introduction we have presented here does not pretend to be exhaustive. On the contrary, we believe that the issues and problems we have showed are complex enough to be solved within the extensions of this work; but also, we believe they are clear enough to open a research program about intention revision.
Acknowledgements. The author would like to thank the anonymous reviewers and Dr. Axel Barcelo for their helpful comments and precise corrections. The author is supported by the CONACyT scholarship 214783.