Knowledge Representation

Lugano course, November 2009

Knowledge Representation1

Knowledge Representation

Grigoris Antoniou

FORTH-ICS, Greece



Week’s Objectives

Get an idea of what Knowledge Representation (KR) is about

Get a taste of the area through a couple of concrete languages/systems

See how KR plays a role in contemporary ICT areas: Web, pervasive computing

Get motivated for more?



Week’s Outline

I. KR Basics

II. KR on the Web: Semantic Web

III. Defeasible Reasoning

IV. KR in e-Commerce and Pervasive Computing

V. Summary



Part I:Knowledge Representation Basics



Artificial Intelligence

The design and study of systems that behave intelligently

– Focus on hard problems, often with no, or very inefficient full algorithmic solution

– Focus on problems that require “reasoning” (“intelligence”) and a large amount of knowledge about the world

Critical:– Represent knowledge about the world– Reason with these representations to obtain meaningful

answers/solutions



Symbolic Knowledge Representation: Basic Assumptions

Important objects (collections of objects) and their relationships are represented explicitly by internal symbols

Symbolic manipulation of internal symbolic representations achieves results meaningful in the real world.



Symbolic Knowledge Representation: Basic Assumptions (2)

SymbolicRepresentation

Real World

New conclusions

Real World

Symbolicrepresentation

Map back to real world

Manipulation



KR Goals

Find representations that are: Rich enough to express the important

knowledge relevant to the problem at hand Close to problem at hand: compact, natural,

maintainable Amenable to efficient computation



Representational Adequacy

Consider the following facts:– Most children believe in Santa.– John will have to finish his assignment before he can

start working on his project.

Can all be represented as a string! But hard then to manipulate and draw conclusions.

How do we represent these formally in a way that can be manipulated in a computer program?



Well-defined Syntax & Semantics

Precise syntax: what can be expressed in the language – Formal language, unlike natural language– Prerequisite for precise manipulation through

computation

Precise semantics: formal meaning of expression



Naturalness of Expression

Also helpful if our representation scheme is quite intuitive and natural for human readers!

Could represent the fact that my car is red using the notation: – “xyzzy ! Zing” – where xyzzy refers to redness, Zing refers to

by car, and ! used in some way to assign properties.

But this wouldn’t be very helpful...



Inferential Adequacy

Representing knowledge not very interesting unless you can use it to make inferences:– Draw new conclusions from existing facts.

“If its raining John never goes out” + “It’s raining today” so...

– Come up with solutions to complex problems, using the represented knowledge.

Inferential adequacy refers to how easy it is to draw inferences using represented knowledge.



Inferential Efficiency

You may be able, in principle, to make complex deductions, but it may be just too inefficient.

The basic tradeoff of all KR:– Generally the more complex the possible deductions,

the less efficient will be the reasoning process (in the worst case).

The eternal quest of KR:– Need representation and inference system sufficient

for the task, without being hopelessly inefficient.



Inferential Adequacy (2)

Representing everything as natural language strings has good representational adequacy and naturalness, but very poor inferential adequacy.



Requirements for KR Languages: Summary

– Representational Adequacy– Clear syntax/semantics– Inferential adequacy– Inferential efficiency– Naturalness

In practice no one language is perfect, and different languages are suitable for different problems.



Why Reasoning?

Example:

Patient x is allergic to medication m

Anybody allergic to medication m is also allergic to medication n

Is it ok to prescribe n for x?

Reasoning uncovers implicit knowledge not represented explicitly– Beyond database systems technology



Syntactic vs Semantic Reasoning

Semantic reasoning:– Sentences P1,…, Pn entail sentence P iff the truth of P is

implicit in the truth of P1, …, Pn– Or: if the world satisfies P1,…, Pn then it must also satisfy P– Reasoning usually done by humans

Syntactic reasoning:– Sentences P1,…, Pn infer sentence P iff there is a syntactic

manipulation of P1,…,Pn that results in P– Reasoning done by humans and machines



Reasoning: Soundness and Completeness

Sound (syntactic) reasoning:– If P is inferred by P1,…, Pn then it is also entailed semantically– Only semantically valid conclusions are drawn

Complete (syntactic) reasoning:– If P is entailed semantically by P1,…, Pn then it can also be

inferred– All semantically valid conclusions can be drawn

Usually interested in sound and complete reasoning– But sometimes we have to give up one for the sake of efficiency

(usually completeness)



Main KR Approaches

Logic-Based– Focus on clean, mathematical semantics:

declarativity– Explainability

Frames / Semantic Networks / Objects– Focus on structure of objects

Rule-based systems– Focus on efficiency– A B in logic and rule-based systems



The Landscape of KR

Predicate logic (first order logic) and its sublanguages– Logic programming, (pure) Prolog– Description logics– Web ontology languages

Predicate logic (first order logic) extensions– Modal and epistemic logics– Temporal logics– Spatial logics

Inconsistency-tolerant logics: – Paraconsistency– Nonmonotonic reasoning



The Landscape of KR (2)

Representing vagueness– Probabilistic logics– Bayesian networks– Markov chains

Planning and reasoning about action– Extensions of logic to reason about the

prerequisites and effects of actions

…



Part II:KR on the Web: Semantic Web



The Semantic Web

The Semantic Web vision RDF OWL Rules



Today’s Web

Most of today’s Web content is suitable for human consumption

– Even Web content that is generated automatically from databases is usually presented without the original structural information found in databases

Typical Web uses today people’s– seeking and making use of information, searching for and

getting in touch with other people, reviewing catalogs of online stores and ordering products by filling out forms



Keyword-Based Search Engines

Current Web activities are not particularly well supported by software tools– Except for keyword-based search engines (e.g.

Google, AltaVista, Yahoo)

The Web would not have been the huge success it was, were it not for search engines



Problems of Keyword-Based Search Engines

High recall, low precision. Low or no recall Results are highly sensitive to vocabulary Results are single Web pages Human involvement is necessary to interpret

and combine results Results of Web searches are not readily

accessible by other software tools



On HTML

Web content is currently formatted for human readers rather than programs

HTML is the predominant language in which Web pages are written (directly or using tools)

Vocabulary describes presentation



An HTML Example

<h1>Agilitas Physiotherapy Centre</h1>Welcome to the home page of the Agilitas Physiotherapy Centre. Do you feel pain? Have you had an injury? Let our staff Lisa Davenport,Kelly Townsend (our lovely secretary) and Steve Matthews take careof your body and soul.<h2>Consultation hours</h2>Mon 11am - 7pm<br>Tue 11am - 7pm<br>Wed 3pm - 7pm<br>Thu 11am - 7pm<br>Fri 11am - 3pm<p>But note that we do not offer consultation during the weeks of the <a href=". . .">State Of Origin</a> games.



Problems with HTML

Humans have no problem with this Machines (software agents) do:

– How distinguish therapists from the secretary, – How determine exact consultation hours – They would have to follow the link to the State Of

Origin games to find when they take place.



A Better Representation

<company><treatmentOffered>Physiotherapy</treatmentOffered><companyName>Agilitas Physiotherapy Centre</companyName><staff>

<therapist>Lisa Davenport</therapist><therapist>Steve Matthews</therapist><secretary>Kelly Townsend</secretary>

</staff></company>



Semantic Web Technologies

Explicit Metadata Ontologies Logic and Inference Agents



Explicit Metadata

This representation is far more easily processable by machines

Metadata: data about data – Metadata capture part of the meaning of data

Semantic Web does not rely on text-based manipulation, but rather on machine-processable metadata



Ontologies

The term ontology originates from philosophy The study of the nature of existence

Different meaning from computer science An ontology is an explicit and formal

specification of a conceptualization



Typical Components of Ontologies

Terms denote important concepts (classes of objects) of the domain

– e.g. professors, staff, students, courses, departments Relationships between these terms: typically class

hierarchies– a class C to be a subclass of another class C' if every

object in C is also included in C' – e.g. all professors are staff members

Value restrictions – e.g. only faculty members can teach courses



Example of a Class Hierarchy



The Role of Ontologies on the Web

Ontologies provide a shared understanding of a domain: semantic interoperability– overcome differences in terminology – mappings between ontologies

Ontologies are useful for the organization and navigation of Web sites



Typical Ontology Use Case: Image Search

A person searches for photos of an “orange ape”

An image collection of animal photographs contains snapshots of orang-utans.

The search engine finds the photos, despite the fact that the words “orange” and “ape” do not appear in annotations



Example Semantic Annotation



chimpanzee

scratchingthe head

youngape08.jpg

activeagent

posture

life stage

Species ontology

WordNet

ICONCLASS

RDF Annotation of A Web Resource

40

great ape

grass landsrain forest

Africa

chimpanzee

geographicalrangesubClassOf

typicalhabitat

Ontologies Describe Concepts Used



Logic versus Ontologies

The previous example involves knowledge typically found in ontologies– Logic can be used to uncover ontological

knowledge that is implicitly given – It can also help uncover unexpected relationships

and inconsistencies Logic is more general than ontologies

– It can also be used by intelligent agents for making decisions and selecting courses of action



The Semantic Web Layer Tower



Semantic Web Layers

XML layer– Syntactic basis

RDF layer– RDF basic data model for facts– RDF Schema simple ontology language

Ontology layer– More expressive languages than RDF Schema– Current Web standard: OWL



Semantic Web Layers (2)

Logic layer – enhance ontology languages further– application-specific declarative knowledge

Proof layer– Proof generation, exchange, validation

Trust layer– Digital signatures– recommendations, rating agencies ….



The Semantic Web




Basic Ideas of RDF

Basic building block: object-attribute-value triple– It is called a statement– Sentence about Billington is such a statement

RDF has been given a syntax in XML– This syntax inherits the benefits of XML– Other syntactic representations of RDF possible



Basic Ideas of RDF (2)

The fundamental concepts of RDF are:– resources– properties– statements



Resources

We can think of a resource as an object, a “thing” we want to talk about– E.g. authors, books, publishers, places, people,

hotels Every resource has a URI, a Universal

Resource Identifier A URI can be

– a URL (Web address) or – some other kind of unique identifier



Properties

Properties are a special kind of resources They describe relations between resources

– E.g. “written by”, “age”, “title”, etc.

Properties are also identified by URIs Advantages of using URIs:

– Α global, worldwide, unique naming scheme– Reduces the homonym problem of distributed data

representation



Statements

Statements assert the properties of resources

A statement is an object-attribute-value triple– It consists of a resource, a property, and a value

Values can be resources or literals – Literals are atomic values (strings)



Three Views of a Statement

A triple A piece of a graph A piece of XML code

Thus an RDF document can be viewed as: A set of triples A graph (semantic net) An XML document



A Set of Triples as a Semantic Net



Basic Ideas of RDF Schema

RDF is a universal language that lets users describe resources in their own vocabularies

– RDF does not assume, nor does it define semantics of any particular application domain

The user can do so in RDF Schema using:– Classes and Properties– Class Hierarchies and Inheritance– Property Hierarchies



Classes and their Instances

We must distinguish between– Concrete “things” (individual objects) in the

domain: Discrete Maths, David Billington etc.– Sets of individuals sharing properties called

classes: lecturers, students, courses etc.

Individual objects that belong to a class are referred to as instances of that class

The relationship between instances and classes in RDF is through rdf:type



Why Classes are Useful

Impose restrictions on what can be stated in an RDF document using the schema

– As in programming languages– E.g. A+1, where A is an array– Disallow nonsense from being stated



Nonsensical Statements disallowed through the Use of Classes

Discrete Maths is taught by Concrete Maths– We want courses to be taught by lecturers only – Restriction on values of the property “is taught by”

(range restriction)

Room MZH5760 is taught by David Billington– Only courses can be taught– This imposes a restriction on the objects to which

the property can be applied (domain restriction)



Class Hierarchies

Classes can be organised in hierarchies– A is a subclass of B if every instance of A is also

an instance of B – Then B is a superclass of A

A subclass graph need not be a tree A class may have multiple superclasses



Class Hierarchy Example



Inheritance in Class Hierarchies

Range restriction: Courses must be taught by academic staff members only

Michael Maher is a professor He inherits the ability to teach from the class of

academic staff members This is done in RDF Schema by fixing the semantics

of “is a subclass of”– It is not up to an application (RDF processing software) to

interpret “is a subclass of”



Property Hierarchies

Hierarchical relationships for properties– E.g., “is taught by” is a subproperty of “involves” – If a course C is taught by an academic staff member A, then

C also involves Α

The converse is not necessarily true– E.g., A may be the teacher of the course C, or – a tutor who marks student homework but does not teach C

P is a subproperty of Q, if Q(x,y) is true whenever P(x,y) is true



Summary of Basic RDF Functionalities

Metadata statements Instances and classes Binary properties Class hierarchies Property hierarchies Domain and range restrictions



The Semantic Web




Reasoning About Knowledge in Ontology Languages

Class membership – If x is an instance of a class C, and C is a

subclass of D, then we can infer that x is an instance of D

Equivalence of classes – If class A is equivalent to class B, and class B is

equivalent to class C, then A is equivalent to C, too



Reasoning About Knowledge in Ontology Languages (2)

Consistency– X instance of classes A and B, but A and B are

disjoint– This is an indication of an error in the ontology

Classification– Certain property-value pairs are a sufficient

condition for membership in a class A; if an individual x satisfies such conditions, we can conclude that x must be an instance of A



Uses for Reasoning

Reasoning support is important for– checking the consistency of the ontology and the

knowledge– checking for unintended relationships between classes– automatically classifying instances in classes

Checks like the preceding ones are valuable for – designing large ontologies, where multiple authors are

involved– integrating and sharing ontologies from various sources



Reasoning Support for OWL

Semantics is a prerequisite for reasoning support Formal semantics and reasoning support are usually

provided by – mapping an ontology language to a known logical formalism– using automated reasoners that already exist for those

formalisms OWL is (partially) mapped on a description logic, and

makes use of reasoners such as FaCT and RACER Description logics are a subset of predicate logic for

which efficient reasoning support is possible



Limitations of the Expressive Power of RDF Schema

Local scope of properties – rdfs:range defines the range of a property (e.g.

eats) for all classes – In RDF Schema we cannot declare range

restrictions that apply to some classes only – E.g. we cannot say that cows eat only plants,

while other animals may eat meat, too



Limitations of the Expressive Power of RDF Schema (2)

Disjointness of classes– Sometimes we wish to say that classes are

disjoint (e.g. male and female) Boolean combinations of classes

– Sometimes we wish to build new classes by combining other classes using union, intersection, and complement

– E.g. person is the disjoint union of the classes male and female



Limitations of the Expressive Power of RDF Schema (3)

Cardinality restrictions– E.g. a person has exactly two parents, a course is

taught by at least one lecturer

Special characteristics of properties– Transitive property (like “greater than”)– Unique property (like “is mother of”)– A property is the inverse of another property (like

“eats” and “is eaten by”)



Three Species of OWL

W3C’sWeb Ontology Working Group defined OWL as three different sublanguages:– OWL Full– OWL DL– OWL Lite

Recent modifications have led to OWL2 with new sublanguages



Summary of Selected Key OWL Functionalities

Equality of classes and properties Important property characteristics: transitive,

functional, inverse Union, intersection and compement of

classes AllValuesFrom(P,D): All values of statements

with property P must be from class D Cardinality constraints



The Semantic Web




Orthogonal Expressivity

Why consider rules?– Well established technology, used in the business

world, natural for many apps

Orthogonal expressivity:– OWL is based on Description Logic– Horn logic is orthogonal w.r.t. DL



What OWL Cannot Express

It is impossible to define classes whose instances are related to another anonymous individual via different property paths.

E.g. “Home workers are those who live and work in the same location.

Easily expressed in Horn logic:homeWorker(X) :-

work(X,Y),live(X,Z), loc(Y,W), loc(Z,W).



What Horn Logic Cannot Express

1. Existential quantification– E.g. All persons have a father.

2. Disjunction / union– E.g. Persons are men or women.

3. Negation / complement– E.g. Men and women are disjoint.



RDFS and Horn Logic

Statement(a,P,b) P(a,b)

type(a,C) C(a)

C subClassOf D C(X) D(X)

P subPorpertyOf Q P(X,Y) Q(X,Y)

domain(P,C) P(X,Y) C(X)

range(P,C) P(X,Y) C(Y)



OWL in Horn Logic

C sameClassAs D C(X) D(X)

D(X) C(X)

P samePropertyAs Q P(X,Y) Q(X,Y)

Q(X,Y) P(X,Y)



OWL in Horn Logic (2)

transitiveProperty(P) P(X,Y), P(Y,Z) P(X,Z)

inverseProperty(P,Q) Q(X,Y) P(Y,X)

P(X,Y) Q(Y,X)

functionalProperty(P) P(X,Y), P(X,Z) Y=Z




(C1 C2) subClassOf D

C1(X), C2(X) D(X)

C subClassOf (D1 D2)

C(X) D1(X)

C(X) D2(X)




(C1 C2) subClassOf D

C1(X) D(X)

C2(X) D(X)

C subClassOf (D1 D2)

Translation not possible!




C subClassOf AllValuesFrom(P,D)

C(X), P(X,Y) D(Y)

AllValuesFrom(P,D) subClassOf C

Translation not possible!




MinCardinality cannot be translated due to existential quantification

MaxCardinality 1 may be translated if equality is allowed

Complement cannot be translated, in general



Part III: Defeasible Reasoning



Defeasible Reasoning

Nonmonotonic Reasoning: Motivation Defeasible Logic: Basic Ideas Defeasible Logic: Properties



New Information

What time do I arrive in Lugano?

– 6:30pm (by bus from Malpensa)

New information: My flight is delayed by an hour

– New answer: 8:30pm!

New information has led to the retraction of my

previous reply: nonmonotonic behaviour



Incomplete Information

Why did it happen?

Actually because I made assumptions (no delay) that

turned out to be wrong

I made these assumptions because:

– I could not have known in advance: certain information is

incomplete

– Otherwise I would be seen to be strange



Incomplete Information on the Web

Business rules deal with incomplete information: – In the absence of information some assumptions

have to be made which lead to conclusions not supported by classical predicate logic.

In Web applications other players may not be able or willing to provide information. – Communication problems– Privacy or security concerns



Inconsistent Information

Classical logics “collapse” in the face of inconsistencies– Everything can be derived

But inconsistencies do happen in real settings– Common when integrating knowledge from various

Web sources

Nonmonotonic reasoning is inconsistency tolerant reasoning



Rules with Exceptions

Natural representation for policies and business rules. Priority information is often implicitly or explicitly

available to resolve conflicts among rules. Potential applications

– Security policies– Business rules– Personalization– Brokering – Bargaining, automated agent negotiations







Defeasible Logics

Rule-based, without disjunction. Classical negation is used in the heads and bodies of

rules– Negation-as-failure is not used but can be emulated

Rules may support conflicting conclusions. Skeptical: Conflicting rules do not fire.

– Consistency is preserved. Priorities on rules may be used to resolve some conflicts

among rules.



Example 1

R1: a

a provable?



Example 1

R1: a +a

Yes (of course)



Example 2

R1: aR2: a

a provable?



Example 2

R1: a -aR2: a -a

No! (sceptical)



Example 3

R1: aR2: aR1>R2

a provable?



Example 3

R1: a +aR2: a -aR1>R2

Yes!



Example 4

R1: a bR2: bR1>R2

b provable?



Example 4

R1: a b -aR2: b +bR1>R2 -b

No, quite the opposite.



Example 5

R1: aR2: aR3: a bR4: a b

b provable?



Example 5

R1: a -aR2: a -aR3: a b -bR4: a b

No (no “floating conclusions”)



Example 6

R1: aR2: aR3: a bR4: b

b provable?



Example 6

R1: a -aR2: a -bR3: a b +bR4: b

Yes (no propagation of ambiguity)



Example 7

R1: aR2: aR3: a bR4: a bR1>R2R4>R3

b or b provable?



Example 7

R1: a +aR2: a -aR3: a b -bR4: a b +bR1>R2R4>R3

b (sequence of conflict resolution important)



Example 8

R1: a eR2: b eR3: c eR4: d ea b c dR1>R3e provable?



Example 8

R1: a e +aR2: b e +bR3: c e +cR4: d e +da b c d -eR1>R3 -eNo (not inferior attack by R4)



Example 9 (Team Defeat)

R1: a e +a

R2: b e +b

R3: c e +c

R4: d e +d

a b c d +e

R1>R3

R2>R4







Important Properties

Consistency: +A and +A cannot be both derived, unless they are already known as certain knowledge (facts)

Coherence: +A and –A cannot be derived from the same knowledge base.

Complexity: Defeasible logic has linear complexity.



Semantic Characterization

Defeasible logic is defined as a proof theory. A more abstract characterization is desirable.

Argumentation semantics: More abstract definition of meaning in terms of arguments (reasoning chains) and their mutual interactions.

Proof theory is sound and complete w.r.t. this semantics



Connection to Logic Programming

Based on the translation of defeasible

theories into logic programs through the well-

studied meta-program of

– Antoniou G., Billington D., Governatori G., Maher

M.J, "A Flexible Framework for Defeasible

Logics", Proc. AAAI/IAAI 2000, AAAI/MIT Press,

pp. 405-410.



The Meta-Program

definitely(X) :- fact(X).definitely(X) :-

strict(R,X, [Y1,...,Yn]),definitely(Y1),...,definitely(Yn).

defeasibly(X) :- definitely(X).defeasibly(X) :-

not definitely(X),supportive_rule(R,X, [Y1,...,Yn]),defeasibly(Y1),...,defeasibly(Yn),not overruled(R,X).



The Meta-Program (2)

overruled(R,X) :-

rule(S,X,[U1,...,Un]),

defeasibly(U1),...,defeasibly(Un),

not defeated(S, X).

defeated(S,X) :-

sup(T,S),

supportive rule(T,X, [V1,...,Vn]),

defeasibly(V1),...,defeasibly(Vn).



The Meta-Program (3)

supportive_rule(Name,Head,Body):-

strict(Name,Head,Body).

supportive_rule(Name,Head,Body):-

defeasible(Name,Head,Body).

rule(Name,Head,Body):-

supportive_rule(Name,Head,Body).

rule(Name,Head,Body):-

defeater(Name,Head,Body).



Part IV: Applications of Defeasible Reasoning



Applications

Semantic brokering Electronic auctions Pervasive computing / ambient intelligence



Motivation

1st generation e-commerce (present)– Buyers and sellers are humans– Catalogue of well-defined commodities – Fixed price purchases by means of credit card

transaction

2nd generation e-commerce (future)– Buyers and sellers are software agents



Background Theory – Brokering

Brokering or matchmaking: process that requires a host to take a query and to return all advertisements which satisfy the requirements specified in the query – Advertisements– Preferences– Brokering Engine

Brokering engine uses a specific technique and performs the matching of preferences with advertisements



Suitability of Defeasible Logic

Formal language with well-understood meaning, a proof theory, model semantics, and argumentation semantics

It is predictable ,explainable and has linear complexity

Sceptical formalism. It does not support contradictory conclusions



Suitability of Defeasible Logic (2)

Natural representation of important features:– Rules with exceptions– Priorities for expressing user preferences



An Apartment Renting Example

Apartments and their properties are the advertisements

The renter’s requirements and preferences are expressed in defeasible logic



User Requirements & Preferences

1. Carlos is looking for an apartment of at least 45m2 with at least 2 bedrooms. If it is on the 3rd floor or higher, the house must have an elevator. Also, pet animals must be allowed.

2. Carlos is willing to pay $300 for a centrally located 45m2 apartment, and $250 for a similar flat in the suburbs. In addition, he is willing to pay an extra $5 per m2 for a larger apartment, and $2 per m2 for a garden.

3. He is unable to pay more than $400 in total. If given the choice, he would go for the cheapest option. His 2nd priority is the presence of a garden; lowest priority is additional space.



Predicates Used in Formalization

size(x,y), where y is the size of apartment x (in m2) bedrooms(x,y), where apartment x has y bedrooms price(x,y), where y is the price for x floor(x,y), where apartment x is on the y-th floor gardenSize(x,y), where apartment x has a garden of

size y lift(x), meaning that there is an elevator in the house

of x pets(x), meaning that pets are allowed in x central(x), meaning that x is centrally located



Predicates Used (2)

acceptable(x), meaning that flat x satisfies Carlos’s requirements

offer(x,y), meaning that Carlos is willing to pay $ y for flat x



Formalization of Requirements

r1: => acceptable(X)

r2: bedrooms(X,Y), Y < 2 => ¬acceptable(X)r3: size(X,Y), Y < 45 => ¬acceptable(X)r4: ¬pets(X) => ¬acceptable(X)r5: floor(X,Y), Y > 2, ¬lift(X) => ¬acceptable(X)r6: price(X,Y), Y > 400 => ¬acceptable(X)r2 > r1, r3 > r1, r4 > r1, r5 > r1, r6 > r1



Formalization of Requirements (2)

r7: size(X,Y), Y ≥ 45, garden(X,Z), central(X) => offer(X, 300 + 2Z + 5(Y−45))

r8: size(X,Y), Y ≥ 45, garden(X,Z),¬central(X) => offer(X, 250 + 2Z + 5(Y−45))

r9: offer(X,Y), price(X,Z), Y < Z => ¬acceptable(X)

r9 > r1



A Sample Collection of Apartments

App Bed Size Cent Floor Lift Pets Gard Price

a1 1 50 yes 1 no yes 0 300

a2 2 45 yes 0 no yes 0 335

a3 2 65 no 2 no yes 0 350

a4 2 55 no 1 yes no 15 330

a5 3 55 yes 0 no yes 15 350

a6 2 60 yes 3 no no 0 370

a7 3 65 yes 1 no yes 12 375



Results of User Requirements

Apartment a1 is not acceptable because it has one bedroom only (rule r2).

Apartments a4 and a6 are unacceptable because pets are not allowed (rule r4).

Apartment a2 is unacceptable because it costs more than the $300 Carlos is willing to pay (rules r7 & r9).

The rest, a3, a5 and a7, are acceptable.



Formalization of User Preferences

r10: acceptable(X), price(X,Z), not(acceptable(Y),

Y X, price(Y,W), W < Z) => cheapest(X)

r11: cheapest(X), gardenSize(X,Z), not(cheapest(Y), Y X, gardenSize(Y,W), W < Z) => largestGarden(X)

r12: largestGarden(X), size(X,Z), not(largestGarden(Y), Y X,

size(Y,W), W < Z) => rent(X)



Results of User Preferences

Apartments a3 and a5 are the cheapest acceptable apartments (rule r10)

a5 is selected because it has larger garden than a3 (rules r11 and r12)



Applications




Auction Strategies

English Auction: One of the most popular one-to-many

negotiation mechanisms Simplest form: multi-party single-issue

negotiation Popular in Internet trading



English Auction Principles

Seller sets reservation price, which may or may not be announced to the bidders

Seller sets timing constraint, – firm deadline, as maximum duration between two

successive bids, or both

Potential buyers then issue increasingly higher bids, with increment threshold



English Auction Principles (2)

Auction stops when the timing constraint is violated – i.e. either the deadline is reached, or no bid

registered for longer than the established maximum duration.

The last bidder then buys the item at the price of the last bid

If no bid above reservation price, the item is not sold



Auction Broker

Standard in online trading communities Registers the parameters of the auction Publishes them Processes incoming bids Continuously makes accessible the auction's

status



A Sample Bidder Strategy

Mark wishes to participate in the auction of an item. He doesn't know exactly how much the item is worth, but he thinks that its value lies somewhere within two bounds L and U. He is keen not to over-value the item, so he decides to assume at the beginning of the auction that the item is worth L, and to eventually increase his valuation whenever one of the following two situations occurs: (a) at least 3 bids above his current valuation have been registered, or (b) somebody has bid more than 20% of his current valuation.



A Sample Bidder Strategy (2)

As soon as one of these conditions is met, Mark will raise his valuation by the minimum possible amount that allows him to stay in the auction. However, he will never accept to valuate the item above U. As it is usual in the case of English auctions, Mark will start by bidding some minimum amount (i.e. the reservation price), and if needed, he will subsequently overbid the other participants' bids by the minimum increment, as long as the resulting bid is less than his current valuation. In the eventuality where the auction's deadline is too close and that he does not hold the current highest bid, he will bid his current valuation instead of just overbidding by the minimum increment.



Predicates & Functions for Auction Description

min_increment denotes the minimum mount by which the bidders are allowed to overbid

initial_bid denotes the minimum amount of the first acceptable bid. (reservation price may be higher, but unknown to bidders)

time_remaining(T) provides the time remaining before the end of the auction

highest_quote(N) provides the current highest bid quotes_above(X, N) holds if N bids above amount X

have been registered.



Predicates & Functions for Bidding Strategy

time_threshold is the duration to the deadline, below which Mark estimates that he should bid his valuation instead of just overbidding by the minimum increment

significant_bidders is the number of bidders that should bid above Mark's current valuation before he considers raising it

significant_increment is the amount (expressed as a percentage), that another bidder should bid above Mark's current valuation before he considers raising it (in working example it is 0,2)



Predicates & Functions for Bidding Strategy (2)

max_valuation is self-explainable submit_bid(X) states that a bid of amount X should

be submitted valuation(X) gives the current valuation while

pre_valuation(X) gives the valuation that was valid at the end of the previous activation of the reasoning module

my_bid(X) gives the amount of the last accepted bid issued by the bidder. At the beginning of the auction my_bid(0) holds



Formalization of Bidding Strategy

r1: my_bid(X), highest_quote(Y), valuation(Z),

X < Y, Y + min_increment < Z,

time_remaining(T), T > time_threshold

submit_bid(Y + min_increment)

If there is enough time remaining and the agent's current bid is not the highest one, it should be increased by the minimum increment, provided that the current valuation allows so.



Formalization of Bidding Strategy (2)

r2: my_bid(X), highest_quote(Y), valuation(Z), X < Y, Y + min_increment < Z, time_remaining(T), T time_threshold submit_bid(Z)

If the deadline is close and the bidder does not hold the item, a bid of the amount of the current valuation should be submitted immediately.




r3: pre_valuation(X) valuation(X)r4: pre_valuation(X), quotes_above(X, N), N significant_bidders, highest_quote(Y) valuation(Y + min_increment)r5: pre_valuation(X), highest_quote(Y), Y > (1 + significant_increment) X

valuation(Y + min_increment)r6: Y > max_valuation ~> valuation(Y)r4 > r3, r5 > r3




Conflicting literals: C(submit_bid(x)) = { submit_bid(y) | y x } C(new_valuation(x)) =

{ new_valuation(y) | y x }




Rules r3 through r6 allow to derive the valuation– r4 and r5 model the two conditions under which

the valuation should be raised – r6 is a defeater modeling the fact that the bidder

is under no circumstances willing to valuate the item above a given amount.



Modularity of the Formalization

Suppose user wants to modify the strategy “raise the valuation if the reservation price has not

been met and the highest bid is above my current valuation”

Just add the rule:r7: reservation_not_met, valuation(X), highest_quote(Y), Y > X valuation(Y + min_increment)r7 > r3



Modularity of the Formalization (2)

We don’t have to worry whether the reservation price is greater than the bidder’s maximum valuation or not.



Applications




Context in Ambient Intelligence

Aim of AmI systems– right information to the right users, at the right time, in

the right place, and on the right device thorough knowledge and understanding of context

Context in Ambient Intelligence– “.. any information that can be used to characterize the

situation of an entity. An entity is a person, place or object that is considered relevant to the interaction between a user and application, including the user and application themselves..” [Dey and Abowd, 1999]



Contextual Reasoning in Ambient Intelligence

Challenges– Imperfect nature of the available context information

Unknown, ambiguous, imprecise, erroneous – Special characteristics of ambient environments

Highly dynamic and open environments Distributed context knowledge Unreliable and restricted wireless communications

Limitations of current AmI systems– No formal model for reasoning with imperfect context– Centralized architectures → No support for distributed

reasoning



Motivating AmI Scenario

Dr. Amber’s phone is configured to take decisions about whether it should ring in case of incoming calls based on its context and Dr. Amber’s preferences:

–The phone should ring, unless it is in silent mode or Dr. Amber is busy with some important activity.

–A lecture at the university is one such important activity.

Dr. Amber is located in the ‘RA201’ university classroom reading his e-mails on his laptop. It is Tuesday, the time is 7.50 p.m., and he has just finished with a lecture for course CS566. His context-aware mobile phone receives an incoming call, but it is not in silent mode.



Motivating AmI Scenarioclass

RA201

one person detectedno class

activity



Scenario Characteristics

Assumptions– each agent aware of the type and quality of imported

knowledge– each agent has some computing and reasoning

capabilities– each agent willing to disclose part of its local knowledge

Challenges– context is incomplete, imprecise, ambiguous – restricted computing capabilities– light communication load for making quick decisions



Multi-Context Systems

Definition– Logical formalizations of distributed context theories

connected through a set of mapping rules, which enable information flow between different contexts

– Context: a logical theory that models local context knowledge

Challenges– Heterogeneity of local context theories– Inconsistencies caused by the interaction of contexts

through the mappings



Global Inconsistency in MCS

Context C

¬kk

Context A

Context B



Modeling the AmI scenario

– Local facts and rules Phone (P1)

r11l : → incoming_call

r12l : → normal_mode

r13l : incoming_call, normal_mode, ¬important_activity → ring

r14l : lecture → important_activity

– Mapping rules r15

m : scheduled(CS566)2, location(RA201)3 lecture

r16m

: ¬class_activity4 ¬ lecture

– Preference relation T1 = [P3, P4, P2]



Modeling the AmI scenario

Laptop (P2)

r21l : → day(Tuesday)

r22l : → time(19.50)

r23l : day(Tuesday), time(X), 19.00 < X < 20.00 →

scheduled(CS566) Localization Service(P3)

r41l : → location(RA201)

Classroom Manager (P4)

r41l : → projector(off)

r42m

: → detected(X)5, X<2, projector(off) ¬ class_activity

Person Detection Service(P5)

r51l : → detected(1)



Future Work

Overlapping vocabularies Access control & privacy mechanisms More applications in the Ambient Intelligence and Semantic

Web domains– Run on small devices– Efficient reasoning is well-suited for real-world and real-

time applications



Part V: Summary



Summary

KR is about difficult problems that cannot be solved directly algorithmically

– Or offers advantages in terms of transparency, modularity and explanation

KR is a multi-faceted area– Always seeking a balance between expressive power and

manageable computational complexity

KR in contemporary ICT areas– Web– Ambient Intelligence



References

The standard textbook on Knowledge Representation: R. Brachman and H. Levesque. Knowledge

Representation and Reasoning. Morgan Kaufmann 2004

The standard textbook on the Semantic Web: G. Antoniou and F. van Harmelen. A Semantic Web

Primer, 2nd ed. MIT Press 2008www.semanticwebprimer.org

A useful page on the semantic web: www.semanticweb.org



References (2)

A textbook on nonmonotonic reasoning: G. Antoniou. Nonmonotonic Reasoning. MIT Press

1997

A paper on defeasible logics: G. Antoniou, D. Billington, G. Governatori and M. Maher.

Representation Results for Defeasible Logic. ACM Transactions on Computational Logic 2,2 (2001): 255-287 http://eprint.uq.edu.au/archive/00002222/01/tocl.pdf



References (3)

A paper on brokering based on defeasible reasoning: G. Antoniou, T. Skylogiannis, A. Bikakis, M. Doerr, N.

Bassiliades. DR-BROKERING: A semantic brokering system. Knowledge-Based Systems 20(1): 61-72 (2007)

lpis.csd.auth.gr/publications/EEE05-a.pdf A paper on defeasible reasoning in ambient

intelligence: A. Bikakis, G. Antoniou, P. Hasssapis. Strategies for Contextual

Reasoning with Conflicts in Ambient Intelligence. Knowledge and Information Systems (forthcoming)

Documents

Knowledge Representation