Knowledge Representation Techniques: A Rough Set Approach

336 Pages·2006·3.59 MB·English

by  Patrick Doherty

PatrickDoherty,WitoldŁukaszewicz,AndrzejSkowron,AndrzejSzałas
KnowledgeRepresentationTechniques
StudiesinFuzzinessandSoftComputing,Volume 202
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Szałas
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KnowledgeRepresentationTechniques:A
FuzzyQuantifiers:AComputationalTheory,
RoughSetApproach,2006
2006
ISBN3-540-33518-8
ISBN3-540-29634-4
Patrick Doherty
Witold Łukaszewicz
Andrzej Skowron
Andrzej Szałas
Knowledge Representation
Techniques
A Rough Set Approach
ABC
ProfessorPatrickDoherty ProfessorAndrzejSkowron
DepartmentofComputer InstituteofMathematics
andInformationScience WarsawUniversity
LinköpingUniversity,Sweden Warsaw,Poland
E-mail:[email protected] E-mail:[email protected]
ProfessorWitoldŁukaszewicz ProfessorAndrzejSzałas
TheUniversityofEconomics TheUniversityofEconomics
andComputerScience andComputerScience
Olsztyn,Poland Olsztyn,Poland
E-mail:[email protected] and
DepartmentofComputer
andInformationScience
LinköpingUniversity,Sweden
E-mail:[email protected]
LibraryofCongressControlNumber:2006924365
ISSNprintedition:1434-9922
ISSNelectronicedition:1860-0808
ISBN-10 3-540-33518-8SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-33518-4SpringerBerlinHeidelbergNewYork
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(cid:1)c Springer-VerlagBerlinHeidelberg2006
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Contents
Part I Introduction and Preliminaries
1 Introduction............................................... 3
2 Basic Notions.............................................. 17
3 Rough Sets ................................................ 39
4 Relational and Deductive Databases ....................... 57
5 Non-Monotonic Reasoning................................. 77
Part II From Relations to Knowledge Representation
6 Rough Knowledge Databases ..............................103
7 Combining Rough and Crisp Knowledge...................129
8 Weakest Sufficient and Strongest Necessary Conditions....143
9 CAKE: Computer Aided Knowledge Engineering ..........159
10 Formalization of Default Logic Using CAKE...............181
11 A UAV Scenario: A Case Study ...........................213
VI Contents
Part III From Sensors to Relations
12 Information Granules......................................229
13 Tolerance Spaces ..........................................245
14 A Rough Set Approach to Machine Learning ..............277
15 UAV Learning Process: A Case Study .....................311
References.....................................................321
Index..........................................................335
1
Introduction
1.1 Background
The basis for the material in this book centers around research done in an
ongoing long-term project which focuses on the development of highly au-
tonomousunmannedaerialvehiclesystems.1Theactualplatformwhichserves
as a case study for the research in this book will be described in detail later
in this chapter. Before doing that, a brief background of the motivations be-
hind this research will be provided. One of the main research topics in the
project is knowledge representation and reasoning and its use in Uav plat-
forms. A very strong constraint has been placed on the nature of research
done in the project where theoretical results, to the greatest extent possible,
should serve as a basis for tractable reasoning mechanisms for use in a fully
deployed autonomous Uav operating under soft real-time constraints associ-
atedwiththetypesofmissionscenariosenvisioned.Consideringthatmuchof
theworkwithknowledgerepresentationinthiscontextfocusesonapplication
domains where one can only hope for an incomplete characterization of such
domains, this methodological constraint has proven to be quite challenging
since, in essence, the focus is on tractable approximate and nonmonotonic
reasoningsystems.Asiswellknown,untilrecently,nonmonotonicformalisms
have had a notorious reputation for lack of tractable and scalable reasoning
systems. At an early stage, a decision was made to investigate a number of
standardnonmonotonicreasoningapproachesandtheircombinationwithap-
proximatereasoningtechniquesbasedontheuseofroughsettheory,oratthe
very least, guided by intuitions from rough set theory. In addition, a decision
was also made to deal seriously with the sense/reasoning gap associated with
moststate-of-the-artroboticsystemswhereitisoftenthecasethathigh-level
reasoning systems are not strongly grounded in the sensory data continually
generated by sensor platforms. Pragmatically, an effort has been made to
1 Uav is an acronym for Unmanned Aerial Vehicles.
P.Dohertyetal.:KnowledgeRepresentation Techniques,Studfuzz202,3–16(2006)
www.springerlink.com (cid:1)c Springer-VerlagBerlinHeidelberg2006
4 1 Introduction
instantiate any new results in the context of traditional relational database
or deductive database technology, with the intention of integrating such sys-
tems on our experimental Uav platforms as stand-alone services which can
be used by other autonomous functionality integrated in the Uav platforms.
Anattempthasalsobeenmadetoshowhowonecouldgroundsuchreasoning
mechanisms in such systems through the use of machine learning techniques
for generating rough relations or classifiers which can then be embedded as
part of the knowledge representations stored in extended database format.
This book contains a cohesive, self-contained collection of many of the theo-
retical and applied research results that have been achieved so far, and which
for the most part pertain to nonmonotonic and approximate reasoning sys-
tems developed for the experimental Uav platforms. The work is far from
complete and the longer term goals have not yet been reached. That being
said, this book provides a foundation for continuing research along the lines
sketched above. Throughout the book, it is more or less assumed that the
backgroundparadigmorframeworkinwhichapproximateandnonmonotonic
reasoning systems can be embedded is that of an agent or multi-agent frame-
work. Although agent architectures are not developed in detail, it is assumed
that each agent will have one or more knowledge bases containing both sta-
tic and dynamic information about itself and its surrounding environment.
From this perspective, an agent can be either a software agent (or softbot),
or an actual physical artifact. In both cases, one would have to deal with
the sense/reasoning gap in order for knowledge representation and inference
mechanisms to be of practical use in such systems. In the following sections,
intelligentartifactsandthesense/reasoninggaparediscussedinfurtherdetail
and an actual physical artifact used in our experimentation is described.
1.2 Intelligent Artifacts and Agents
The use of intelligent artifacts, both at the workplace and in the home, is
becoming increasingly more pervasive due to a number of factors which in-
clude the accessibility of the Internet/World-Wide-Web to the broad masses,
the drop in price and increase in capacity of computer processors and mem-
ory, and the integration of computer technology with telecommunications.
Intelligentartifactsareman-madephysicalsystemscontainingcomputational
equipment and software that provide them with capabilities for receiving and
comprehendingsensorydata,forreasoning,andforperformingrationalaction
in their environment. The spectrum of capabilities and the sophistication of
an artifact’s ability to interface to its environment and reason about it varies
withthetypeofartifact,itsintendedtasks,thecomplexityoftheenvironment
in which it is embedded, and its ability to adapt its models of the environ-
ment at different levels of knowledge abstraction. Representative examples of
intelligent artifacts ranging from less to more complex would be mobile tele-
1.3 Knowledge Representation 5
phones,personaldigitalassistants(PDAs),softbotsontheWorld-Wide-Web,
collections of distributed communicating artifacts which serve as components
of smart homes, mobile robots, unmanned aerial vehicles, and many more.
One unifying conceptual framework that can be used to view these increas-
inglymorecomplexintegratedcomputersystemsisassocietiesofagents(vir-
tuallyand/orphysicallyembeddedintheirrespectiveenvironments)withthe
capacity to acquire information about their environments, structure the in-
formation and interpret it as knowledge, and use this knowledge in a rational
manner to enhance goal-directed behavior which is used to achieve tasks and
to function robustly in their dynamic and complex environments.
1.3 Knowledge Representation
An essential component in agent architectures is the agent’s knowledge rep-
resentationcomponentwhichincludesavarietyofknowledgeanddatarepos-
itories with associated inference mechanisms. The knowledge representation
component is used by the agent to provide it with models of its embedding
environment and of its own and other agent capabilities, in addition, to rea-
soning efficiently about them. It is becoming increasingly important to move
away from the notion of a single knowledge representation mechanism with
one knowledge source and inference method to multiple forms of knowledge
representation with several inference methods. This viewpoint introduces an
interesting set of complex issues related to the merging of knowledge from
disparate sources and the use of adjudication or conflict resolution policies to
provide coherence of knowledge sources (see also Chapter 9).
Duetotheembeddednatureoftheseagentsocietiesincomplexdynamicenvi-
ronments,itisalsobecomingincreasinglyimportanttotakeseriouslythegap
between access to low-level sensory data and its fusion and integration with
more qualitative knowledge structures. These signal-to-symbol transforma-
tions should be viewed as an on-going process with a great deal of feedback
between the levels of processing. In addition, because the embedding envi-
ronments are often as complex and dynamic as those faced by humans, the
knowledge representationswhichareusedasmodelsoftheenvironmentmust
necessarily be partial, elaboration tolerant and approximate in nature.
Figure 1.1 provides a schematic of the sense/reasoning gap. In any robotic
system or complex agent system, there is a continual flow of data throw the
system and much processing along the way. As sensor data is input into an
agent system, more traditional sensor fusion techniques are used to construct
quantitative models used for navigation or to control manipulators. For so-
phisticated autonomous behavior, these models are not adequate due to the
limited temporal horizons assumed and the limited predictive or anticipa-
tory capability which can be derived from such models. Intelligent behavior
6 1 Introduction
...
(cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3)
Qualitative reasoning
 
Incomplete,  (cid:3) (cid:3)  Qualitative
...
inconsistent Databases
 
data (cid:3) (cid:3)
Quantitative reasoning
 
Noisy,  (cid:3) ... (cid:3)  Quantitative
incompdlaettae  (cid:1) (cid:1) (cid:1) ... (cid:2) (cid:2) (cid:1) DSeantsaobrasses
cameras,...
Fig. 1.1. Sense/reasoning gap.
requires more complex qualitative models which are constructed from prop-
erties of entities and relations between entities. Such entities can be physical
or epistemic. Generally, neither complete information about entities, nor suf-
ficient and necessary conditions for relations are present in the models that
can be constructed from noisy and incomplete sensor data. So there is a flow
of data from and into quantitative to combined quantitative/qualitative to
qualitative structures which is a necessary part of any robotic architecture.
Research in this book is structured along the lines depicted in the figure, one
partwhichtakesusfromsensordatatorelationsofaquantitative/qualitative
nature and another part which takes us from these relations to more com-
plex qualitative knowledge representations useful for robotic agents. In re-
lated work, more pragmatic issues which deal with the practical distributed
data flowmanagement through complex robotic architectures has beeninves-
tigated, but will not be covered in this book.
Concept Acquisition and Fluid Knowledge Structures
Just as an agent’s surrounding environment is in flux, so are many of its
knowledgestructures.Forexampleapproximate relationsmayinitially bede-
fined with very weak sufficient and/or necessary conditions, but as the agent
learnsmoreaboutitsenvironmenttheseconditionsmaybetightenedandeven
sometimes loosened. The grounding of approximate concepts and relations is
contextual and based on the quality and quantity of sensory data at hand.
Part of the approach pursued in this book, is to develop a framework for the
specification, implementation and management of fluid knowledge structures