emerging trends in ict security || using event reasoning for trajectory tracking

CHAPTER

16Using Event Reasoning forTrajectory Tracking

Jianbing MaBournemouth University, Bournemouth, UK

INFORMATION IN THIS CHAPTER

• Event model

• Scenario adapts

• Event functions and inference rules

• Experiments

INTRODUCTION

During the past decade, there has been massive investment in CCTV technology in the UK.

Currently, there are approximately four million CCTV cameras operationally deployed. Despite

this, the impact on anti-social and criminal behavior has been minimal. Although most incidents,

also called events, are captured on video, there is no response because very little of the data is

actively analyzed in real time. Consequently, CCTV operates in a passive mode, simply collecting

enormous volumes of video data. For this technology to be effective, CCTV has to become active

by alerting security analysts in real time so that they can stop or prevent the undesirable behavior.

Such a quantum leap in capability will greatly increase the likelihood of offenders being caught, a

major factor in crime prevention.

To ensure in-time reaction for intelligent surveillance [1,2], one fundamental task to utilize

CCTV videos is to track the trajectory of any subject of interest (e.g., [3,4], etc.). This trajectory

knowledge is very powerful as an input to future reasoning, but even on its own it would allow us

to augment traditional CCTV monitoring displays. For example, rather than just present a human

operator with a live CCTV image of a subject, we could also augment the live feed with a series of

key timestamped frames taken at other points in the facility.

253Emerging Trends in ICT Security. DOI: http://dx.doi.org/10.1016/B978-0-12-411474-6.00016-5

© 2014 Elsevier Inc. All rights reserved.

http://dx.doi.org/10.1016/B978-0-12-411474-6.00016-5

ExampleConsider a subject with the intent of leaving a suitcase with an explosive device in a crowded air-

port space and leaving before detonation. The CCTV operator is shown a live video feed of the

subject exiting the airport through a recognized exit at time T. However, using our trajectory track-

ing, the live feed can also be supplemented with earlier footage of the subject entering the airport

at time T - 4 minutes. Conceivably, the operator might also be shown a representation or map of

the route taken by the subject through the space. Crucially, by comparing the images, the operator

observes that the subject entered with a suitcase (from the archived frames) but left with no bag-

gage (from the live frames). This could warrant an alert.

This example shows that the short-term historical details are extremely valuable to the human

operator by putting a live feed into a wider context.

Key to the success of subject tracking is subject reacquisition [5]. That is, when we have

detected a subject, we should be able to know who it is by retrieving from our subject database on

past records. Currently, common approaches for subject acquisition are face recognition and cloth-

ing color signature classification, etc.

We should notice that in some testing scenarios, these methods can behave well, but they are

facing major challenges in real application.

Face recognition can give a pretty precise result for cooperative subjects (that is, a subject looks

at the camera for a few seconds with the face clearly exposed) within a small subject database.

When the size of the subject database increases, there will be a considerable decline in the preci-

sion of face recognition, since the possibility that subjects with similar face features increases. This

problem can be alleviated by improving face recognition algorithms. Clothing color signature

method only applies when we assume that the subject does not change clothes while in the environ-

ment. Most importantly, pure video analytic approaches can be hard to apply or the results can be

not enough to obtain a clear trajectory when there are not enough cameras or when some cameras

have been tampered with.

While video analytics alone are not sufficient to obtain a clear trajectory, we are aware that

there is usually more information that can be used in tracking, for example, (identity) card reading

results, topological information about the environment, etc. These kinds of dynamic information (e.

g., video analytics, card reading results, etc.) and background information (e.g., it takes a person

30 seconds to walk from location A to location B) can be combined by event reasoning [6,7]

techniques.

The aim of this chapter is to successfully determine a subject’s passage through a series of mon-

itored spaces, given the following scenario. Some spaces (called zones) have sensors capable of

making observations about the physical location of a subject at a given time and observing key

appearance signatures of a subject at a given time (facial features, clothing color, etc.). Some zones

have no sensors. We have domain knowledge regarding the topology of connecting zones and we

have expected time-of-flight information for subjects moving between zones. Access to some zones

is protected by access control hardware. It should be noticed that this chapter focuses more on aug-

menting trajectory information by using background information than on computing accurate paths

by some trajectory tracking efforts, such as in [8,9], etc.

To this end, in this chapter, event reasoning techniques are introduced to integrate information

from various sources, for example, video analytics, card reading results, domain knowledge, etc.

254 CHAPTER 16 Using Event Reasoning for Trajectory Tracking

The main idea is to use inference rules to infer the passage of a subject when there is not enough

dynamic information. Another focus of this chapter is how to obtain a precise identity of a subject.1

That is, when a subject is detected by a camera, how to classify it as one of a subject already in

our database, since a camera can only detect a subject, not recognize a subject. Here the detector is

a combination of the camera and the video analytics, while the recognition results follow the rea-

soning process.

In the literature, event reasoning systems have been proposed for dealing with event composi-

tion in many areas, such as those discussed in [10�13], etc. This chapter extends frameworks pro-

posed in [10,11] to allow event functions. We also have simplification settings with respect to the

frameworks in [10,11], especially for rule definitions. Subsequently, in the “Event Model” section,

we introduce our event model. In the section titled “Scenario Adapts,” we adapt event settings with

respect to the application practice. “Event Functions and Inference Rules” shows event functions

and rules used in the application. Experimental results are provided in the “Experiments” section.

In the summary, we conclude the chapter.

Event modelIn this section, we introduce an event reasoning model that is a variant of the event reasoning

framework proposed in [10,11] to adapt our scenario.

Event definitionIn this chapter, we distinguish two kinds of events: observable events and domain events. An

observable event is an occurrence that is instantaneous (event duration is 0, i.e., takes place at a

specific point in time) and atomic (it happens or not). The atomic requirement does not exclude

uncertainty. For instance, when there is a person entering a building who can be Bob or Chris based

on face profiling, then whether it is Bob or Chris who enters the building is an example of uncer-

tainty. But Bob (resp. Chris) is entering the building is an atomic event that either occurs

completely or does not occur at all. To represent uncertainty encountered during event detection, in

the following, we distinguish an observation (with uncertainty) from possible events associated

with the observation (because of the uncertainty). This can be illustrated by the above example: an

observation is that a person is entering the building and the possible observable events are Bob is

entering the building and Chris is entering the building. An observation says that something hap-

pened, but the subject being observed is not completely certain yet, so we have multiple observable

events listing who that subject might be.

This event definition is particularly suitable for surveillance, where the objects being monitored

are not complete clear to the observer.

1It is called “subject reacquisition” in the video analysis community. In this chapter, subject determined by inference is

somehow beyond this meaning. But for simplicity, we will still call it subject reacquisition.

255Event model

Event representationA concrete event definition in this special application is defined as follows:

occT: the point in time that an event occurred

location: the 3-D location that an event occurred

pID: the classified person ID of that event

iID: the information source ID that reports that event

This format is specially designed for our subject tracking scanario. Here a subject is the human

entity detected in the event. We don’t know who it is, so we should determine the subject’s identity

by subject reacquisition (SR). However, SR techniques usually cannot provide us precise classifica-

tion results; instead, it yields several possible candidates. As in this application, our dynamic infor-

mation comes from either face recognition, clothing color recognition, pure localization, or card

reading; iID hence can be one of the following values: {face, color, loc, card}. In addition, we will

introduce a kind of inferred event, which also follows this definition, but its iID is infer.

Formally, we define an event e as: e5 (occT, location, pID, iID).

Event clusterAny two events with the same occT location, and iID are from the set of possible events related to

a single observation. For example, e15 (20:01:00, 13.5/12.5/0, Bob, face) and e25 (20:01:00,

13:5/12.5/0, Chris, face) are two possible events from a single observation. To represent these,

event cluster, denoted as EC, is introduced, which is a set of events that have the same occT, loca-

tion, and iID, but with different pID values. Events e1 and e2 above form an event cluster for the

observed fact that a subject is entering the building at 20:01:00 at location 13.5/12.5/0.

An event is always attached to a probability, and we use p(e) to denote the probability of e.

For an event e in event cluster EC, we use notations like e.occT to denote the time of occur-

rence of e, etc. By abuse of notations, we also write EC.occT to denote the time of occurrence of

any event in EC, etc., since all the events in EC share the same values on these attributes.

Probabilities for events in an event cluster EC should satisfy the normalization condition:

’eAECpðeÞ5 1. That is, EC does contain an event that really occurred. For example, for the two events,

e1 and e2, introduced above, a possible probability function p can be p(e1)5 0.85 and p(e2)5 0.15.

An event cluster hence gives a full description of an observed fact with uncertainty from the

perspective of one source.

Event functionsEvent functions are functions applied on events to get required results. For instance, a simple but

useful function EC(e, e0) is a boolean function that determines whether two events e and e0 are in

the same event cluster.

ECðe; e0Þ5 ðe:occT5 e0:occTXe:location5 e0:locationXe:iID5 e0:iIDÞSome event functions are generic to any application (e.g., EC(e, e0)) while some event functions

may only be proposed for special applications. To our knowledge, the notion of event functions has

not been proposed by any event reasoning frameworks in the literature.


Event inferenceEvent inference is expressed as a set of rules that are used to represent the relationships between

events. An inference rule R is formatted as:

If cond1and cond2

and cond3

?then action1

Conditions can be evaluated by known information of current events and other assertions about

the environment/situation. If all conditions are evaluated as true, then action1 can be taken, which

usually sets values for some events or raises alerts, etc.. An example of the rule is as follows:

If e1.occT5 e2.occT

and e1.location 6¼ e2.location

and e1.pID5 e2.pID

and e1.iID5 infer

and e2.iID5 infer,

then RaiseAlert

The conditions of this rule are that, at the same time but in different locations, there are two

inferred events indicating that two subjects are the same person. Obviously this is impossible, so if

all these conditions hold, an alert should be raised to the monitor.

Scenario adaptsIn this section, we introduce the details of dynamic events generated in this scenario, including

face or clothing color recognition events, localization events, and card reading events.

Video sensor observations generate observation events, and in the application these observations

have the following primary attributes:

• A timestamp

• A face signature

• A color signature

• A localization (in the image plane)

Face recognition, color histogram matching, and localization algorithms generate the following

secondary attributes:

• An n-best list of face matches

• An n-best list of color histogram matches

• A localization (in the real world)

Here, an n-best list of matches means that a subject is being classified as several candidate per-

sons, with associated probabilities derived by video analytic algorithms (namely face recognition

algorithm, color matching algorithm, etc.). For instance, a subject can be classified as: Bob with

257Scenario adapts

probability 0.65, Chris with probability 0.2, and David with probability 0.15. Note that either an

n-best list of face matches or an n-best list of color matches generates an event cluster.

Overall, we find that these resulted events by algorithms can be described by our event defini-

tion given previously. That is, we have occT , location (real world), pID (each taken from the

n-best lists), and iID (face or color), which perfectly matches our event definition. In addition, these

events are attached with probabilities.

In practice, for the sake of computational efficiency, we cannot afford always recording facial

or clothing color information and applying corresponding algorithms. Hence, most of the time, we

only apply localization sensing that records only the location of a subject. The ratio of facial/color

recognition events and pure localization events are about 1:5 to 1:10, etc. A localization event has

the following primary attributes:

• A timestamp

• A localization (in the image plane)

A localization event can generate the following secondary attributes:

• An n-best list of matches (using the closest facial or clothing matching results)

• A localization (in the real world)

Since the ratio of facial/color recognition events and pure localization events are about 1:5 to

1:10, etc., we can always find a nearest facial/color recognition event cluster with the same subject

ID. As there can be two closest event clusters (i.e., one for face recognition and the other for cloth-

ing color), we select the event cluster that contains a greatest probability. After obtaining the clos-

est n-best matches, the localization events form an event cluster. For example, if the two nearest

event clusters are: e15 (20:01:00, 13.5/12.5/0, Bob, face) with probability 0.85, e25 (20:01:00,

13.5/12.5/0, Chris, face) with probability 0.15, and e015 (20:01:00, 13.5/12.5/0, Bob, color) with

probability 0.55, e025 (20:01:00, 13.5/12.5/0, David, color) with probability 0.45, then the localiza-

tion event cluster will take the face matching results as its n-best list of matches for the events in

the event cluster.

Access control events, or card reading events, have the following attributes:

• A timestamp

• A unique card identity reference

• A location (of the access control panel)

Secondary attributes of this event are:

• A user identity (name of the card owner)

• Other employee details; however, we should ignore these in this case for clarity.

For a card reading event, we will set its subject ID sID to a special value, ANY, which matches

any subject ID. Therefore, we also have the required occT, location, sID, pID, and iID values. The

probability is 1.

Environment topological information, or more generally, background information (also called

domain knowledge), is seen mostly about the expected time-of-flight information for subjects mov-

ing between zones; that is, the time a person took to go from one zone to another. For instance, a

person cannot appear within zone A and then appear in zone B within 10 seconds. But if the 10 s is


changed to 10�20 seconds, then it could be possible; if the time-of-flight is 20�40 seconds, it is

highly possible; if the time is greater than 40 seconds, it is possible, etc. Empirical probabilities for

such information can be found by tests. However, we will use simple settings that in some special

range of time-of-flight, the certainty is 1 instead of probabilities.

AssumptionsOur ultimate objective aims at complicated environments. However, initially, we will begin with

simple scenarios with simplification assumptions. Complexity can be incrementally increased. This

process clarifies our objective. Some initial assumptions are listed below:

• Only one subject shall be considered (no occlusions, etc.).

• The subject will be cooperative at key points (i.e., look into the camera for a few frames).

• The subject will not change clothing for the duration of the scenarios.

• The subject swiping the access card can be assumed to be the registered owner of the card

(i.e., not stolen or cloned).

Event functions and inference rulesIn this section, we introduce the event functions and inference rules used in this application.

First, we define some useful event functions. The next event with the same classified person is

defined as:

NextðeÞ5 e1 : e1:iID 6¼ inferXe:occT , e1:occTXe:pID5 e1:pIDX='e2:

e:occT , e2:occT , e1:occTXe:pID5 e2:pID:

Here recall that “infer” is the iID of an inferred event.

Given the Next(e) function, similarly, a Prev(e) function that obtains the very previous event of

e with the same subject can be defined as:

PrevðeÞ5 e1 : e5Nextðe1Þ:Note that Prev(e) only defines for dynamic events. It is not defined for inferred events.

We also define a local function Neighbor(e, e0) to judge whether e and e0 are neighbors with

respect to space and time.

Neighbor e; e0ð Þ5 ðabsðe:occT 2 e0:occTÞ, 0:1 secXdis e:location; e0:locationð Þ, 0:5m

Here, dis is a measure of distance between two locations.

The following function judges whether e is the very last event that appears on ground floor.

That is, any event exactly next to it is not on ground floor.

GroundLastðeÞ5ðe:location:z5GROUNDFloorX='e0ðe05nextðeÞXe0:location:z5GROUNDFloorÞÞ

Here GROUNDFloor is a predefined application constant. Note that this function is a special

one for this application.

259Event functions and inference rules

Another important event function is to create an event.

CreateðoccT ; location; pID; iID; xÞ5 ðe : e5 ðoccT ; location; pID; iIDÞ and pðeÞ5 xÞNote that only inferred events can be created. Based on the dynamic (video, card information,

etc.) information and background information, we can set up rules to infer which person it is.

First, we list rules for inferring a KnownSubjectAcquired event, which is a special kind of event

used for indicating the most possible candidate of a subject. The iID value of a

KnownSubjectAcquired event e5 (occT, location, pID, iID) is set to infer. Also note

KnownSubjectAcquired events are not attached to an event cluster.

Rules for inferring KnownSubjectAcquired events are listed as follows:

• If e1.iID 6¼ infer and p(e1). 0.5 and / 'e2 (EC(e1; e2) Xp(e1)2 p(e2), 0.3) , then Create

(e1.occT, e1.location, e1.pID, infer, p(e1)).

• If e1.iID5 card, then Create(e1.occT, e1.location, e1.pID, infer, 1).

• If e1.iID5 infer and e2.iID 6¼ infer and Neighbor(e1,e2) and e1.pID5 e2.pID and e2.pID. 0.5,

then Create(e2.occT, e2.location, e2.pID, infer, p(e2)).

• If e1.iID5 infer and e2.iID5 infer and Neighbor(e1,e2) and e1.pID 6¼ e2.pID and p(e1). p(e2)

and 'e3((e35Prev(e1)We35Next(e1))Xe3.occT5 e2.occTXe3.location5 e2.location), then e2.

pID5 e1.pID, p(e2)5 p(e1).

Note that rule 1 implies that if a dynamic event has an associated probability of at least 0.65,

then it must satisfy conditions of rule 1. Rule 2 takes advantage of no-stolen and no-clone assump-

tion of cards. Rule 3 indicates that if some subject has been reacquired, then the subject in the

neighbor event is also him/her. This rule makes use of the one-subject-at-a-time assumption and is

shown satisfied, in most cases. Also, it is proved very useful and powerful in reasoning. Rule 4 is

used to resolve inconsistency. That is, if two neighbor events provide different classifications, then

the more reliable one should be respected.

There are also rules for inferring KnownSubjectAcquired events that use background knowl-

edge. For instance, we use event reasoning rules to judge whether a person takes a lift or goes from

the stairway when he is found at the first floor.

• If e1.iID 6¼ infer and dis(e1.location, LIFTLocation), 1 m and e1.pID5 e2.pID and e1.

location.z5GROUNDFloor and e2.location.z5FIRSTFloor and 0, e2.occT2 e1.

occT, 5 sec, then Create((e1.occT1 e2.occT)/2, INLIFT, e2.pID, infer, 1).

If e1.iID 6¼ infer and GroundLast(e1) and e1.pID5 e2.pID and e1.location.z5 (GROUNDFloor

and e2.location.z5FIRSTFloor and e2.occT2 e1.occT. 10 sec, then Create ((e1.occT1 e2.

occT)/2, INSTAIR, e2.pID, infer, 1).

• If e1.iID 6¼infer and GroundLast(e1) and e1.pID5 e2.pID and e1.location.z5GROUNDFloor

and e2.location.z5FIRSTFloor and 8, e2.occT2 e1.occT ,5 10 sec and dis(e1.location,

STAIRLocation), 1 m, then Create ((e1.occT1 e2.occT)/2, INSTAIR, e2.pID, infer, 1).

• If e1.iID 6¼ infer and e1.iID 6¼ infer and e1.pID5 e2.pID and dis(e1.location, WCLocation), 1 m

and dis(e2.location,WCLocation), 1 m and e2.occT2 e1.occT. 60 sec and e25 next(e1), then

Create((e1.occT1 e2.occT)/2, INWC, e2.pID, infer, 1).

Here LIFTLocation, FIRSTFloor, INLIFT, WCLocation and INWC are predefined application

constants. The first rule says if a subject first appears on the ground floor and then is detected at


the first floor within five seconds, then the subject must have taken a lift. The second and third rule

indicate how to judge whether the subject uses the stairway to go to the first floor. The last rule

tells that if a subject goes to and leaves the WC (the lavatory) for one minute and does not appear

anywhere during that period, then the subject must be in the WC. In addition, similar rules can be

set up for subjects who go down from the first floor, etc.

There can be many such rules using topological and time-of-flight information of the environment.

There are also rules for inferring inconsistencies between events. Usually, an inconsistency indi-

cates a potential system failing and warranting investigation. An example rule is:

If e1.iID5 infer and e2.iID5 infer and e1.pID5 e2.pID and dis(e1.location; e2.location). 10� abs(e1.occT2 e2.occT), then RaiseAlert.

Here RaiseAlert is a system function to alert the monitor, or it just acts as a report of system

failure.

A trajectory can be set up by tracing KnownSubjectAcquired events, which provides more infor-

mation than video analytic results.

The system architecture is shown in Figure 16.1.

KnownSubject

AcquiredEvent

KnownSubject

AcquiredEvent

Inference

Trajectory

Inference

Card Reading

BackgroundInformation

VideoAnalytics

FIGURE 16.1

Using event reasoning for trajectory.

261Event functions and inference rules

ExperimentsWe demonstrate our system by the following scenario, showing that we can infer trajectories of

subjects even if we do not have clear images in some zones. This experiment scenario shows that

our method can be used to enhance security.

Consider: five subjects sequentially enter a building, with their faces (as our cooperative subject

assumption) detected, analyzed, and recognized (with a high certainty). They move in, with only

their clothing color signature being detected (with a medium or low certainty). After some time,

they are detected on the first floor. They swipe their cards and go to their offices, which are captured

by cameras in the corridors. They go to the WC occasionally. Finally, they leave the building.

Video analytics only provide clear information when the subjects are cooperatively looking at

the cameras, and card reading can only prove the identity of the card owner at the moment of card

swiping. However, even for cooperative subjects, sometimes video analytic algorithms make wrong

classifications. Figures 16.2, 16.3, and 16.4 show some video dynamic information on face recogni-

tion and clothing color signature.

In this experiment, we compare the clear information provided by dynamic information only,

and by our event reasoning systems.

FIGURE 16.2

Video analytic results.


For this experiment, the performance is characterized by the true positive rate: TPR5N/NPR,

where NPR is the number of pieces of clear information in which the subject has been correctly classi-

fied and N is the total number of pieces of clear information in which the subject is classified.

We applied the methods on the scenario previously proposed. The comparison results are pre-

sented in Table 16.1.

The generated dynamic events include 5 card reading events, 10 face recognition events at the

ground floor, 5 face recognition events at the first floor, and 20 clothing color recognition events,

of which there are 8 mis-classifications. The generated 348 pieces of clear information include

40 dynamic events, 280 localization events (ratio 1:7), 10 subject going up events, 10 subject going

down events, and 8 WC events, in which the mis-classification events are due to the original video

mis-classification. But some mis-classifications are fixed by rule 4 proposed in the above section.

From Table 16.1, we can see that an event reasoning system provides much more clear informa-

tion about the trajectory of the subject. It is not surprising because, with event reasoning, we can pro-

vide clear information for localization events and other tracking events when there are no cameras

(e.g., the subject is in WC, etc.). We can also see that the event reasoning system gives an increase

of approximately 11 percent in TPR compared to that provided by dynamic information only. This is

because the mis-classification of cooperative subjects can be corrected by neighbor classifications.

FIGURE 16.3


263Experiments

SummaryIn this chapter, we propos an event reasoning system which can help to track the trajectory of sub-

jects. We set up rules to infer which subject is seen based on uncertain video analytic results. We

also infer the position of subjects when there is no camera data by using topological information of

environments. This framework has been evaluated by a simulated experiment, which shows a better

performance than using video analytic results only.

FIGURE 16.4


Table 16.1 Comparison of TPR for Dynamic Information Only and for Event

Reasoning System

Methods N NPR TPR (%)

Dynamic 40 32 80

Event Reasoning 348 316 91


We find that the advantage of using event reasoning in these scenarios are two-fold:

• Event reasoning helps to determine which subject is tracked when we have uncertain video

analytic results.

• Event reasoning helps to determine the route the subject passes when we have no video

analytic results.

For future work, we want to extend this event reasoning model to include the expression of

incomplete information using probability theory (induced from combining knowledge bases

[14,15]) or Dempster-Shafer theory [16�19]. Also, we need to consider cases where a combination

of some uncertain results can provide more certain results. In addition, we will gradually loosen

our assumptions to allow multiple subjects to appear at the same time, allow non-cooperative sub-

jects, allow unreliable card information, etc. Furthermore, situation calculus [20,21] can be used to

keep a record of the events. Belief revision [22�27] and merging [28�31] techniques for uncertain

input can also be considered in our framework.

AcknowledgmentsThis research work is sponsored by the EU Project: 251617 (the INFER project) and EPSRC projects

EP/D070864/1 and EP/G034303/1 (the CSIT project).

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[16] Ma J, Liu W, Dubois D, Prade H. Revision rules in the theory of evidence. In: Procs of ICTAI; 2010.

p. 295�302.

[17] Ma J, Liu W, Dubois D, Prade H. Bridging Jeffrey’s rule, AGM revision and Dempster conditioning in

the theory of evidence. Int J Artif Intell Tools 2011;20(4):691�720.

[18] Ma J, Liu W, Miller P. A characteristic function approach to inconsistency measures for knowledge

bases. In: Procs of SUM; 2012. p. 473�85.

[19] Ma J. Measuring divergences among mass functions. In: Procs of ICAI; 2013.

[20] Ma J, Liu W, Miller P. Belief change with noisy sensing in the situation calculus. In: Procs of UAI;

2011.

[21] Ma J, Liu W, Miller P. Handling sequential observations in intelligent surveillance. In: Proceedings of

SUM; 2011. p. 547�60.

[22] Ma J, Liu W. A general model for epistemic state revision using plausibility measures. In: Procs of

ECAI; 2008. p. 356�360.

[23] Ma J, Liu W. Modeling belief change on epistemic states. In: Procs of FLAIRS; 2009.

[24] Ma J, Liu W. A framework for managing uncertain inputs: An axiomization of rewarding. Int J Approx

Reasoning 2011;52(7):917�34.

[25] Ma J, Liu W, Benferhat S. A belief revision framework for revising epistemic states with partial episte-

mic states. In: Procs of AAAI; 2010. p. 333�8.

[26] Ma J, Benferhat S, Liu W. Revising partial pre-orders with partial pre-orders. A unit-based revision

framework; 2012.

[27] Ma J, Benferhat S, Liu W. Revision over partial pre-orders: A postulational study. In: Procs of SUM;

2012. p. 219�32.

[28] Ma J, Liu W, Hunter A. The non-Archimedean polynomials and merging of stratified knowledge bases.

In: Procs of ECSQARU; 2009. p. 408�20.

[29] Ma J, Liu W, Hunter A. Modeling and reasoning with qualitative comparative clinical knowledge. Int J

Intell Syst 2011;26(1):25�46.

[30] Ma J, Liu W, Hunter A, Zhang W. An XML based framework for merging incomplete and inconsistent

statistical information from clinical trials. In: Soft Computing in XML Data Management; LNAI; 2010.

p. 259�90.

[31] Ma J, Liu W, Hunter A, Zhang W. Performing meta-analysis with incomplete statistical information in

clinical trials. BMC Med Res Methodol 2008;8(1):56.
























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