POSSIBILISTIC ACTIVITY RECOGNITION

Patrice C. Roy

, Bruno Bouchard

, Abdenour Bouzouane

and Sylvain Giroux

Domus laboratory, Université de Sherbrooke, Sherbrooke, Canada

LIAPA laboratory, Université du Québec à Chicoutimi, Chicoutimi, Canada

Keywords:

Ambient intelligence, Activity recognition, Possibilistic description logic, Smart homes, Cognitive assistance.

Abstract:

The development towards ambient computing will stimulate research in many ﬁelds of artiﬁcial intelligence,

such as activity recognition. To address this challenging issue, we present a formal activity recognition frame-

work based on possibility theory, which is largely different from the majority of all recognition approaches

proposed that are usually based on probability theory. To validate this novel alternative, we are developing an

ambient agent for the cognitive assistance of an Alzheimer’s patient within a smart home, in order to identify

the various ways of supporting him in carrying out his activities of daily living.

1 INTRODUCTION

Combining ambient assisted living with techniques

from activity recognition greatly increases its accep-

tance and makes it more capable of providing a better

quality of life in a non-intrusive way. Elderly peo-

ple, with or without disabilities, could clearly beneﬁt

from this new technology (Casas et al., 2008). Ac-

tivity recognition aims to recognize the actions and

goals of one or more agents from a series of obser-

vations on the environmental conditions. Due to its

many-faceted nature, research addressing the recog-

nition problem in smart environments refer to activ-

ity recognition as plan recognition, which relates be-

haviours to the performer’s goals. The plan recogni-

tion problem has been an active research topic (Au-

gusto and Nugent, 2006) for a long time and still

remains very challenging. The keyhole, adversarial

or intended plan recognition problem (Geib, 2007)

is usually based on a probabilistic-logical inference

for the construction of hypotheses about the possible

plans, and on a matching process linking the observa-

tions with some activity models (plans) related to the

application domain.

Prior works have been done to use sensors, like

radio frequency identiﬁcation (RFID) tags attached

to household objects (Philipose et al., 2004), to rec-

ognize the execution status of particular types of

activities, such as hand washing (Mihailidis et al.,

2007), in order to provide assistive tasks like, for in-

stance, reminders about the activities of daily living

(ADL) (Pollack, 2005). However, most of these re-

searches has largely focused on probabilistic models.

One limitation of probability theory is that it is in-

sufﬁcient to handling imperfect information, which is

impressed of uncertainty and imprecision. In the con-

text of cognitive assistance, where the human agent

is characterized by erratic behaviours, complete ig-

norance about the speciﬁc dependence between two

actions cannot be represented with the classical prob-

ability theory. The possibility theory (Dubois and

Prade, 1988), an alternative to probability theory, is

an uncertainty theory devoted to the handling of in-

complete information. By using a pair of dual set-

functions (possibility and necessity measures) instead

of one, this theory allows us to capture partial igno-

rance, so that it is possible to represent partial belief

about events. Also, it is more easier to capture partial

belief concerning the activities realization from hu-

man experts, since this theory was initially meant to

provide a graded semantics to natural language state-

ments (Zadeh, 1978).

At the Domus and LIAPA labs, we investigate

possibility theory to address this issue of recogniz-

ing behaviours classiﬁed according to cognitive er-

rors. These recognition results are used to iden-

tify the various ways a smart home may help an

Alzheimer’s occupant at early-intermediate stages to

carry out his ADLs. This context increases the recog-

nition complexity in such a way that the presumption

of the observed agent’s coherency, usually supposed

in the literature, cannot be reasonably maintained. We

184

C. Roy P., Bouchard B., Bouzouane A. and Giroux S. (2010).

POSSIBILISTIC ACTIVITY RECOGNITION.

In Proceedings of the 2nd International Conference on Agents and Artiﬁcial Intelligence - Artiﬁcial Intelligence, pages 184-189

DOI: 10.5220/0002701801840189

 SciTePress

propose a formal framework for activities recogni-

tion based on description logic and possibility theory,

which transforms the recognition problem into a pos-

sibilistic classiﬁcation of activities. The possibility

and necessity measures on behaviour hypotheses al-

low us to capture the fact that, in some case, erroneous

behaviours concerning the realization of activities can

be equally possible than normal behaviours. Hence,

in a complete ignorance setting, both behaviour types

are fully possible, where each type is not necessarily

the one being carried out. So, unlike probability the-

ory, possibility theory is not additive.

The paper is organized as follows. Section 2

presents our new possibilistic recognition model.

Section 3 presents an overview of related work. Fi-

nally, we conclude the paper by outlining future plans

with this work.

2 POSSIBILISTIC ACTIVITY

RECOGNITION MODEL

In our model, the observer agent has knowledge

concerning the resident’s environment, which is

represented by using a formalism in description

logic(DL) (Baader et al., 2007). DL is a family

of knowledge representation formalisms that may be

viewed as a subset of ﬁrst-order logic, and its expres-

sive power goes beyond propositional logic, although

reasoning is still decidable. By using the open world

assumption, it allows us to represent the fact that the

environment is partially observable. The observation

of the environment’s state with sensors allows us to

obtain the low–level context C of the environment.

Since, the observation can be partial, this context can

represent a subset of the environment’s state space S

(C ⊆ S), where states of this subset share some com-

mon environmental properties. For instance, the con-

text where the patient is in the kitchen, the pantry door

is open, and the pasta box is in the pantry includes

several possible states. Also, a set of contexts can be

a partition of the environment’s state space.

In order to infer behavioural hypotheses about the

realization of activities by an observed patient, the no-

tion of possibilistic actions must be formalized, since

activities are carried out by performing a sequence of

actions that affect the environment’s state. A possi-

bilistic action on the set of environment’s states S is a

nondeterministic action where the transitions between

states are quantiﬁed with a possibility distribution.

Deﬁnition 2.1 (Possibilistic Action). A possibilistic

action a is a tuple (C

pre

pos

,π

init

,π

trans

), where

pre

and C

pos

are context sets and π

init

and π

trans

are possibility distributions.

pre

is the set of possible contexts before the ac-

tion occurs (pre–action contexts), C

pos

is the set of

possible contexts after the action occurs (post–action

contexts), π

init

is the possibility distribution on C

pre

that an environment’s state in a particular context al-

lows the action to occur, and π

trans

is the transition

possibility distribution between contexts in C

pre

and

pos

if the action does occur.

The action library is represented with an ontology,

where the set of possible actions A is partially ordered

with the action subsumption relation ⊑

, which can

be seen as an extension of the concept subsumption

relation ⊑ of DL (Baader et al., 2007).

Proposition 2.2 (Action subsumption). Let a, b ∈ A

be two action tuples (C

pre

, C

pos

, π

init

, π

trans

) and

pre

, C

pos

, π

init

, π

trans

). If an action b is sub-

sumed by an action a, denoted by b ⊑

a, then for

all context d in C

pre

, there exists a context c in C

pre

where d ⊑ c, π

init

(d) 6 π

init

(c), and for each con-

text e in C

pos

, there exists a context f in C

pos

where

e ⊑ f and π

trans

(e|d) 6 π

trans

( f|c).

For instance, the OpenDoor action subsumes the

OpenPantryDoor action, where the OpenDoor is at

least as possible than OpenPantryDoor in contexts

where OpenPantryDoor can be carried out or ob-

served.

With this action library, the recognition agent

evaluates the most possible action that can explain

the changes observed in the environment. An obser-

vation at a time t, denoted by obs

, consists to a set

of DL assertions describing, according to the sensors,

the environment’s state resulting from an action re-

alization. Since the observation obs

can be partial,

multiple contexts c

can be entailed by this observa-

tion (obs

|= c

), which inﬂuences the possibility and

necessity measures of observation for each action.

To determine such possibility and necessity mea-

sures of action observation, a possibility distribution

on the action library concerning the possibility that a

particular action was observed according to the previ-

ous action prediction possibilities (possibility that an

action will be the next one carried out) and the cur-

rent action recognition possibilities (possibility that

an action is the one that was carried out) must be eval-

uated. The action prediction possibility distribution

at a time t, π

pre

, is obtained by selecting, for each

action a ∈ A , the maximum possibility value among

the action initiation possibilities π

init

) for the pre–

action contexts c

∈ C

pre

entailed by the observation

obs

. The action recognition possibility distribution at

a time t, π

rec

, is obtained by selecting, for each action

a ∈ A , the maximum possibility value among the ac-

tion transition possibilities π

trans

) for the pre–

contexts c

∈ C

pre

entailed by the previous observa-

POSSIBILISTIC ACTIVITY RECOGNITION

185

tion obs

t−1

and the post–contexts c

∈ C

pos

entailed

by the current observation obs

. Since the prediction

possibilities must be taken into account when evalu-

ating the action observation possibilities, the obser-

vation addition operator ⊕

obs

is used on the previous

prediction possibility distribution π

pre

t−1

and the cur-

rent recognition possibility distribution π

rec

to com-

pute the current action observation possibility distri-

bution π

obs

. The ⊕

obs

operator selects, for each ac-

tion a ∈ A , the maximum possibility value between

the prediction possibility π

pre

t−1

(a) and the recogni-

tion possibility π

rec

(a), in order to obtain the obser-

vation possibility π

obs

(a).

So, for each observation obs

, we evaluate the ac-

tion observation possibility distribution π

obs

, which

allows us to select the most possible observed action

at the time t, according to the possibility and neces-

sity measures of action observation, Π

obs

and N

obs

Those measures, which allow us to indicate the possi-

bility Π

obs

(Act) and necessity N

obs

(Act) that an ac-

tion a in a subset Act ⊆ A ({a} is also a subset) was

observed by the observer agent, according to the en-

vironment’s state described obs

, are given by:

obs

(Act) = max

a∈Act

(π

obs

(a)), (1)

obs

(Act) = max

{b∈A }

(π

obs

(b)) − Π

obs

(Act), (2)

= min

a/∈Act



max

{b∈A }

(π

obs

(b)) − π

obs

(a)



. (3)

obs

(Act) is obtained by taking the maximum value

among the observation possibilities π

obs

(a) of the ac-

tions a in Act. N

obs

(Act) is obtained by taking the

minimum possibility value among the values result-

ing from the subtraction of the maximum value in

the distribution (since it can be not normalized, i.e. at

least one value at 1) with the observation possibilities

obs

(a) of the actions a not in Act (a ∈ Act).

By obtaining the possibility and necessity mea-

sures for each action, we can then select the most pos-

sible observed action a

that can explain the changes

in the environment’s state, described by the obser-

vation obs

, resulting from the realization of an ac-

tion at time t. An observed action at time t, de-

noted by a

, is obtained by selecting the most pos-

sible and necessary action a ∈ A according to the

obs

(a) and N

obs

(a) values. If there is more than

one most possible action, the least common subsumer

action, according to the action subsumption relation,

of this action subset is selected as the observed ac-

tion a

. For instance, if the most possible actions are

OpenTap, OpenColdTap and OpenHotTap, then the

OpenTap action is selected since it subsumes both

OpenColdTap and OpenHotTap. The new observed

action a

is sent to the behaviour recognition agent,

which uses the sequence of observed actions to in-

fer behaviour hypotheses concerning the realization

of the patient’s activities.

Such activities are deﬁned as plan structures,

which consist of a planned sequence of actions that

allows to accomplish the activity’s goals.

Deﬁnition 2.3 (Activity). An activity α is a tuple

(Act

,◦

rel

,π

rel

), where Act

⊆ A is the activ-

ity’s set of actions, which is partially ordered by a se-

quence relation ◦

∈ Act

× Act

× T × T , where T

represents a set of time values, C

rel

is the set of pos-

sible contexts related to the activity realization, and

rel

is the possibility distribution that a context is re-

lated to the execution of the activity.

The use of time values allow us to describe the

minimum and maximum delays between the real-

ization of two actions. So, the ◦ relation, which

is transitive, can be seen as an ordering relation-

ship with temporal constraints between two actions

in the activity plan. For instance, the activity

WatchTv can have an activity plan composed of the

actions SitOnCouch, OpenTv and CloseTv and the

sequence relations (SitOnCouch, OpenTv, 0, 5) and

(OpenTv, CloseTv, 5, 480) (do not watch tv for more

than 8 hours) , where the time values are in minutes.

By using the observation obs

, we evaluate, for

each activity plan α in the plan library P , the pos-

sibility value that the current observed environment’s

state is related to the realization of an activity α. The

activity realization possibility distribution is obtained

by taking, for each activity plan α ∈ P , the maxi-

mum possibility value among the context possibilities

rel

) for the contexts c

∈ C

rel

entailed by the ob-

servation obs

As previously mentioned, the most possible action

that could explain the changes in the environment’s

state according to the observation obs

resulting from

an action realization is sent to the behaviour recog-

nition agent, which uses the sequences of observed

actions to generate hypotheses concerning the be-

haviour of the patient when he performs some activi-

ties. This sequence of observed actions forms an ob-

served plan P

obs

, which consists to a totally ordered

set (a

,...,a

), where each a

is the most possi-

ble and necessary observed action for the observation

obs

. For instance, the observed plan ((OpenDoor,t =

0,3), (EnterKitchen,t = 1,4)) indicates that for obs

the OpenDoor action was observed at a timestamp of

3 minutes after the start of the recognition process,

and for obs

, the EnterKitchen action was observed

one minute later (timestamp of 4 minutes).

Since the current observed behaviour can contain

partial or complete coherent realizations of some ac-

tivity plans, we must deﬁne the notion of partial ex-

ICAART 2010 - 2nd International Conference on Agents and Artificial Intelligence

186

ecution path. A partial execution path Path

Exe

for

an activity plan α is a subset of the observed plan

obs

, where each observed action in the partial path

is associated to an action in the activity plan α. Also,

the observed actions in the partial path Path

Exe

must

represent a coherent realization of a part of the activ-

ity plan, where the sequence and temporal constraints

deﬁned in the activity plan must be respected accord-

ing to the observed actions in the partial path. For

instance, for the observation plan ((SitOnCouch,t =

0,4), (OpenElectricalAppliance,t = 1,5)), possi-

ble partial paths for the WatchTv activity plan could

be the SitOnCouch action only or the SitOnCouch

action followed by the OpenElectricalAppliance

action (since OpenElectricalAppliance subsumes

OpenTv).

At each new observed action a

added to the ob-

served plan P

obs

, the set of partial execution paths

Path

Exe

is updated by extending, removing, or adding

partial paths. A partial path can be extended ifthe new

observed action a

subsumes one of the next possible

actions in the activity plan and if the extended partial

path respects the constraints in the activity plan. If

we can extend a partial path, we must keep a copy of

the original partial path, since the new observed ac-

tion could be not associated to the realization of the

partial path’s activity plan. A partial path is removed

if the maximum delays for the next possible action in

the activity plan are exceeded. A partial path is added

is the observed action a

subsumes one of the ﬁrst ac-

tions in the activity plan.

The set of partial execution paths Path

Exe

is then

used to generate behavioural hypotheses B , according

to the observed plan P

obs

, concerning the observed

behaviour of the patient when he realize some activi-

ties. A behaviour hypothesis b ∈ B for an observed

plan P

obs

is a subset of the partial execution path

set Path

Exe

that respects the following conditions: (i)

each partial path is associated with a different activ-

ity, (ii) some observed actions can be shared between

partial paths, (iii) each partial path must at least have

one action that is not shared. It should be noted that it

is possible that some observed actions in the observed

plan are not in the partial paths.

A behaviour hypothesis is normal, denoted by b

when each observed action in the observed plan is as-

sociated to at least one partial path. A normal be-

haviour represents a coherent realization, which can

be partial or complete, of some activities by the pa-

tient. A behaviour hypothesis is erroneous, denoted

by b

, when some observed actions in the observed

plan are not associated to a partial path. An erroneous

behaviour represents an erroneousrealization of some

activities, while some others activities can still be car-

ried out in a coherent way.

From this point, the behaviour recognition agent

has determined the sets of plausible normal and er-

roneous hypotheses, B

and B

, concerning the be-

haviour of the observed patient. In order to circum-

scribe the behaviour hypothesis set before sending

theses hypotheses to an assistance agent, the possi-

bility and necessity measures concerning the obser-

vation of each behaviour must be evaluated. Such

measures are obtained from the behaviour possibil-

ity distribution, which also need the partial execution

path possibility. The partial execution path possibility

distribution at time t, π

Exe

, is obtained by selecting,

for each partial path p ∈ Path

Exe

, the maximum val-

ues between the minimum action prediction possibil-

ity among the next possible actions and the minimum

value among the action observation and activity pos-

sibilities for each observed action in the partial path.

This partial path possibility distribution π

Exe

is then

used to evaluate the behaviour possibility distribution

bev

. The behaviour possibility distribution π

bev

obtained by selecting, for each behaviour hypothe-

sis b ∈ B , the maximum possibility value between

the minimum partial path possibility for the partial

paths of the behaviour, the minimum action observa-

tion possibility for the observed actions in the partial

paths of the hypothesis, and the minimum action ob-

servation possibility for the observed actions not in

the partial paths of the hypothesis.

The behaviour possibility distribution π

bev

allows

us to evaluate the possibility and necessity measures

of behaviour observation, Π

bev

and N

bev

. Those

measures, which allow us to indicate the possibility

bev

(Bev) and necessity N

bev

(Bev) that a behaviour

b in a subset Bev ⊆ B is the behaviour of the observed

patient according to the observed plan P

obs

, are given

by:

bev

(Bev) = max

{b∈Bev}

(π

bev

(b)), (4)

bev

(Bev) = max

{c∈B }

(π

bev

(c)) − Π

bev

(Bev) (5)

= min

{b/∈Bev}



max

{c∈B }

(π

bev

(c)) − π

bev

(b)



. (6)

bev

(Bev) is obtained by selecting the maximum be-

haviour possibility among the behaviours b in the be-

haviour subset Bev ⊆ B . N

bev

(Bev) is obtained by

selecting the minimum possibility among the values

resulting from the subtraction of the maximum pos-

sibility in the distribution with the behaviour possi-

bilities π

bev

(b) of the behaviour hypotheses b not in

Bev (b ∈ Bev). This allows to represent an interval

of conﬁdence [N

bev

(Bev), Π

bev

(Bev)] concerning the

possibility that a hypothesis behaviour b ∈ Bev is the

POSSIBILISTIC ACTIVITY RECOGNITION

187

observed behaviour of the patient according to the ob-

served plan P

obs

. So, after each observation obs

, the

behaviour recognition agent selects the most possible

and necessary behaviour hypotheses and sends them

to an assistance agent, which will use it to plan an

assistive task if needed.

By using the formal tools previously presented,

we can formulate the Algorithms 1 and 2, which de-

scribe the principal steps in the recognition process.

Algorithm 1 Action recognition.

Input:

obs

, obs

t−1

previous and current observations

pre

t−1

previous action prediction distribution

C context set

t−1

previous entailed contexts

A , P action and plan libraries

Output:

current recognized observed action

pre

, π

rec

, π

obs

, π

rel

current action prediction, action

recognition, action observation, and activity possibility

distributions

1: C

← evaluateEntailedContexts(C ,obs

)

2: π

pre

← evaluateActionPrediction(A , C

)

3: π

rec

← evaluateActionRecognition(A , C

, C

t−1

)

4: π

obs

← observationAddOperator(π

pre

t−1

, π

rec

)

5: a

← selectObservedAction(A , π

obs

)

6: π

rel

← evaluateActivityRelated(P , C

entail

)

To recognize the behaviour of the observed patient

after the realization of an action at a time t, the recog-

nition agent uses the environmental observations obs

to generate behavioural hypotheses that could explain

the sequence of t observed actions. According to the

Algorithm 1, the contextsC

t−1

andC

that are entailed

by the previous and current observations obs

t−1

and

obs

are used to evaluate the action observation possi-

bility distribution π

obs

on the action library A by us-

ing the observation addition operator ⊕

obs

on the pre-

vious action prediction possibility distribution π

pre

t−1

and the action current recognition possibility distri-

bution π

rec

. This action observation possibility dis-

tribution π

obs

is then used to evaluate the action ob-

servation possibility and necessity measures Π

obs

and

obs

, which are used, in conjunction with the action

subsumption relation, to select the most possible and

necessary observed action a

. Also, the activity pos-

sibility distribution π

rel

on the activity plan library

P , which indicates the possibility that the observed

environment’s state described in obs

is related to a

speciﬁc activity realization, is evaluated.

According to the Algorithm 2, the observed plan

obs

, which include the new observed action a

, is

used to generate a set of hypotheses B concerning

the observed behaviour of the patient. The observed

plan P

obs

is used to update the set of partial execu-

Algorithm 2 Behaviour recognition.

Input:

current recognized action observed

obs

t−1

previous observed plan

A , P action and plan libraries

pre

, π

obs

, π

rel

sets of possibility distributions

Path

Exe

partial execution path set

Output:

obs

current observed plan

Path

Exe

updated partial path set

B current behaviour hypotheses

bev

current behaviour possibility distribution

set of most possible behaviour hypotheses

1: P

obs

← appendObservedAction(a

, P

obs

t−1

)

2: Path

Exe

← updatePartialPathSet(Path

Exe

,P , P

obs

)

3: B ← generateBehaviourHypotheses(PathExe, P

obs

)

4: π

Exe

← evalPartialPath(Path

Exe

obs

, π

pre

, π

obs

, π

rel

)

5: π

bev

← evaluateBehaviourPossibility(B , π

Exe

, π

obs

)

6: B

← selectBehaviourHypotheses(B ,π

bev

)

tion paths Path

Exe

, where each partial path is a par-

tial (or complete) coherent realization of an activity

plan. The set of behaviour hypotheses B is obtained

by selecting subsets of Path

Exe

that respect the con-

ditions in order to be a behaviour hypothesis. Each

behaviour hypothesis b ∈ B can be a coherent real-

ization of some activities (b ∈ B

) or an erroneous

realization of some activities (b ∈ B

), according to

its partial path subset and the observed plan. The be-

haviour possibility distribution π

bev

is then evaluated

by using the previous deﬁned possibility distributions

(π

pre

, π

obs

, π

rel

) and the partial execution path pos-

sibility distribution π

Exe

. This behaviour possibility

distribution π

bev

allows us to rankthe set of behaviour

hypotheses B according to the behaviour possibility

and necessity measures Π

bev

and N

bev

. The recogni-

tion agent sends the most possible behaviour hypothe-

ses B

to an assistance agent, which plans an assis-

tance task if needed.

3 RELATED WORK

A number of researchers have investigated activity

recognition as plan recognition. Logical based ap-

proaches (Kautz, 1991) deﬁne a theory using ﬁrst–

order logic, in order to formalize the recognition

activity into an inference process. But to allevi-

ate to the equiprobability problem of logical models,

where an hypothesis cannot be privileged within the

set of possible activities, probabilistic models (Liao

et al., 2004; Philipose et al., 2004), mainly Bayesian

or Markovian based, or hybrid models (Avrahami-

Zilberbrand and Kaminka, 2007; Geib, 2007; Roy

et al., 2009), that use logical and probabilistic reason-

ICAART 2010 - 2nd International Conference on Agents and Artificial Intelligence

188

ing, were proposed. The limit of the vast majority of

these previous approaches is that they were focused

exclusively on the concept of probability where the

inference itself requires large numbers of prior and

conditional probabilities. For example, in the context

of assistive cognition within smart homes, requiring

humans to specify the habitat’s object involvement

probabilities is time consuming and difﬁcult when

we consider all the potential objects involved in each

stage of an activity, given the large numbers of activ-

ities performed. Moreover, the probabilities do not

allow us to represent complete ignorance; besides,

there are numerous situations where it is not possi-

ble to give the agent probabilities based on statistical

measures, but only qualitative information provided

by expertsor deduced frompreviousexperiences. Our

proposed model, by using possibility theory, allows to

mitigate those limitations by taking into account par-

tial belief and by handling the behaviour hypotheses

as a partially ordered set.

4 CONCLUSIONS

This paper has presented a formal framework of ac-

tivities recognition based on possibilistic DL as the

semantic model of the observed agent’s behaviour.

This framework constitutes a ﬁrst step toward a more

expressive ambient agent recognizer, which will fa-

cilitate to support the fuzzy and uncertainty con-

straints inherently to the smart environment. Cur-

rently, the proposed is under implementation in the

software framework of our smart home infrastructure,

which consists of a standard apartment with a kitchen,

living room, dining room, bedroom, and bathroom,

equipped with multiple sensor devices. Moreover, the

next logical step consists in conducting an extension

of this framework inorder to simultaneously dealwith

the vagueness of an activity’s duration and the noises

of the sensors. Finally, we clearly believe that consid-

erable future work and large scale experimentations

will be necessary, in a more advanced stage of our

work, to help evaluate the effectiveness of the model

in the ﬁeld.

REFERENCES

Augusto, J. C. and Nugent, C. D., editors (2006). Design-

ing Smart Homes: The Role of Artiﬁcial Intelligence,

volume 4008 of LNAI. Springer.

Avrahami-Zilberbrand, D. and Kaminka, G. A. (2007).

Utility-based plan recognition: an extended abstract.

In Proc. of AAMAS’07, pages 858–860.

Baader, F., Calvanese, D., McGuinness, D. L., Nardi, D.,

and Patel-Schneider, P. F., editors (2007). The De-

scription Logic Handbook: Theory, Implementation,

and Applications. Cambridge University Press, sec-

ond edition.

Casas, R., Marín, R. B., Robinet, A., Delgado, A. R., Yarza,

A. R., Mcginn, J., Picking, R., and Grout, V. (2008).

User modelling in ambient intelligence for elderly and

disabled people. In Proc. of the 11th ICCHP, number

5105 in LNCS. Springer-Verlag.

Dubois, D. and Prade, H. (1988). Possibility Theory: An

Approach to Computerized Processing of Uncertainty.

Plenum Press.

Geib, C. (2007). Plan recognition. In Kott, A. and McE-

neaney, W. M., editors, Adversarial Reasoning: Com-

putational Approaches to Reading the Opponent’s

Mind, pages 77–100. Chapman & Hall/CRC.

Kautz, H. A. (1991). A formal theory of plan recognition

and its implementation. In Allen, J. F., Kautz, H. A.,

Pelavin, R. N., and Tenenberg, J. D., editors, Reason-

ing About Plans, chapter 2, pages 69–126. Morgan

Kaufmann.

Liao, L., Fox, D., and Kautz, H. (2004). Learning and infer-

ring transportation routines. In Proc. of the AAAI’04,

pages 348–353.

Mihailidis, A., Boger, J., Canido, M., and Hoey, J. (2007).

The use of an intelligent prompting system for peo-

ple with dementia: A case study. ACM Interactions,

14(4):34–37.

Philipose, M., Fishkin, K. P., Perkowitz, M., Patterson,

D. J., Fox, D., Kautz, H., and Hähnel, D. (2004). In-

ferring activities from interactions with objects. IEEE

Pervasive Computing: Mobile and Ubiquitous Sys-

tems, 3(4):50–57.

Pollack, M. E. (2005). Intelligent technology for an aging

population: The use of AI to assist elders with cogni-

tive impairment. AI Magazine, 26(2):9–24.

Roy, P., Bouchard, B., Bouzouane, A., and Giroux,

S. (2009). A hybrid plan recognition model

for Alzheimer’s patients: Interleaved–erroneous

dilemma. Web Intelligence and Agent Systems: An

International Journal, 7(4):375–397.

Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of

possibility. Fuzzy Sets and Systems, 1(1):3–28.

POSSIBILISTIC ACTIVITY RECOGNITION

189