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Master of Science in Artificial Intelligence, 2009-2011
Knowledge Representation
and Reasoning
University "Politehnica" of Bucharest
Department of Computer Science
Fall 2009
Adina Magda Florea
Lecture 1
Lecture outline
 Course goals
 Grading
 Textbooks and readings
 AI well known companies
 Syllabus
 Why KR?
 KR&R Challenges
 What is KR&R?
 Formal logic: why and how
 Links for the young researcher
Course goals
 Provide an overview of existing representational
frameworks developed within AI, their key
concepts and inference methods.
 Acquiring skills in representing knowledge
 Understanding the principles behind diferent
knowledge representation techniques
 Being able to read and understand research
literature in the area of KR&R
 Being able to complete a project in this research
 Course grades
Mid-term exam
Final exam
 Requirements: min 7 lab attendances, min 50% of term
activity (mid-term ex, projects, lab)
 Academic Honesty Policy
It will be considered an honor code violation to give or
use someone else's code or written answers, either for
the assignments or exam tests. If such a case occurs,
we will take action accordingly.
Textbooks and Readings
 Textbooks
• Artificial Intelligence: A Modern Approach (2003,
2009) by Stuart Russell and Peter Norvig
• Computational Intelligence: a Logical Approach by
David Poole, Alain Mackworth, and Randy Goebel,
Oxford University Press, 1998
 Readings
• Reading materials will be assigned to you.
• You are expected to do the readings before the class
AI well known companies
 Cycorp, Inc.
Cycorp was founded in 1994 to research, develop, and commercialize
Artificial Intelligence. Cycorp's vision is to create the world's first true
artificial intelligence, having both common sense and the ability to
reason with it.
 Soar Technology, Inc.
Design of "highly human" intelligent agents
 Autonomous Decision Making Software
 Franz Inc.
Enterprise Development Tools (Allegro CL)
Semantic Web Technologies (AllegroGraph, RacerPro)
Drive Syllabus
1. General knowledge representation issues
2. Logical agents – Logical knowledge representation and
• First order predicate logic revisited, ATP – Lect. 2
AIMA Chapter 7
• Nonmonotonic logics and reasoning – Lect. 4
Non-monotonic Logic, Stanford Encyclopedia of Philosophy
Nonmonotonic Reasoning, G. Brewka, I. Niemela, M. Truszczynski
Nonmonotonic Reasoning With WebBased Social Networks
• Modal logic, logics of knowledge and beliefs – Lect 5
Readings: Modal logic on Wikipedia
+ to be announced
• Semantic networks and description logics, reasoning
services – Lect 6
Readings: to be announced
• Knowledge representation for the Semantic Web –
Lect. 7
Ontology knowledge representation - from description logic to OWL
Description Logics as Ontology Languages for the Semantic Web
Midterm exam (written examination) – 1h
3. Rule based agents
• Rete: Efficient unification – Lect. 8
The RETE algorithm
• The Soar model, universal subgoaling and chunking –
Lect. 9, 10
A gentle introduction to Soar, an architecture for human cognition
• Modern rule based systems – Lect. 11
4. Probabilistic agents
• Probabilistic knowledge representation and reasoning
– Lect. 12
to be announced
• Rule based methods for uncertain reasoning – Lect.
to be announced
5. Intelligence without representation and reasoning
vs. Strong AI – Lect. 14
Final exam (oral examination)
Why KR?
 We understand by "knowledge" all kinds of
facts about the world.
 Knowledge is necessary for intelligent
behavior (human beings, robots).
 What is knowledge? We shall not try to
answer this question!
 Instead, in this course we consider
representations of knowledge and how we
can use it in making intelligent artifacts.
KR&R Challenges
 Challenges of KR&R:
• representation of commonsense knowledge
• the ability of a knowledge-based system to
tradeoff computational efficiency for accuracy
of inferences
• its ability to represent and manipulate
uncertain knowledge and information.
What is KR?
Randall Davis, Howard Shrobe, Peter Szolovits, MIT
 A knowledge representation is most
fundamentally a surrogate, a substitute
for the thing itself, used to enable an entity
to determine consequences by reasoning
about the world.
 It is a set of ontological commitments,
i.e., an answer to the question: In what
terms should I think about the world?
What is KR?
 It is a fragmentary theory of intelligent
reasoning, expressed in terms of three
• the representation's fundamental
conception of intelligent reasoning;
• the set of inferences the representation
• the set of inferences it recommends.
What is KR?
 It is a medium for pragmatically efficient
computation, i.e., the computational
environment in which reasoning is
• One contribution to this pragmatic efficiency is
supplied by the guidance a representation provides
for organizing information so as to facilitate making
the recommended inferences.
 It is a medium of human expression, i.e., a
language in which we say things about the
What is KR?
 If A represents B, then A stands for B and
is usually more easily accessible than B.
 We are interested in symbolic
 Symbolic representations of propositions
or statements that are believed by some
What is Reasoning?
 Not interested (in the course) in the
philosophical dimension
 Reasoning is the use of symbolic
representations of some statements in
order to derive new ones.
 While statements are abstract objects,
their representations are concrete objects
and can be easily manipulated.
What is Reasoning?
 Reasoning can be as easy as mechanical
symbol manipulation.
 or as
 Reasoning should scale well: we need
efficient reasoning algorithms.
Formal logic
 Formal logic is the field of study of entailment
relations, formal languages, truth conditions,
semantics, and inference.
 All propositions/statements are represented as
formulae which have a semantics according to
the logic in question.
 Logical system = Formal language +
 Formal logics gives us a framework to discuss
different kinds of reasoning.
Logical consequence (entailment)
 Proof centered approach to logical
consequence: the validity of a reasoning
process (argument) amounts to there
being a proof of the conclusions from the
Logical consequence (entailment)
 Model centered approach to logical
 Models are abstract mathematical structures that
provide possible interpretations for each of the
non-logical primitives in a formal language.
 Given a model for a language - define what it is
for a sentence in that language to be true
(according to that model) or not.
 In any model in which the premises are true the
conclusion is true too. (Tarski's definition of logical
consequence from 1936.)
Properties of logical systems
Important properties of logical systems:
 Consistency - no theorem of the system contradicts
 Soundness - the system's rules of proof will never
allow a false inference from a true premise. If a system
is sound and its axioms are true then its theorems are also guaranteed to
be true.
 Completeness - there are no true sentences in the
system that cannot, at least in principle, be proved
in the system.
 Some logical systems do not have all three properties. Kurt Godel's
incompleteness theorems show that no standard formal system of
arithmetic can be consistent and complete.
Important notions in logical systems
 Model of a formula
 Entailment or logical implication
 Theorem, deduction
 Th() – set of provable theorems in 
Idempotence - multiple applications of the operation do not
change the result
 Th() – a fixed point operator which computes the
closure of a set of formulas  according to the rules of
 Th() – the least fixed point of this closure process
 Important theorems for entailment
Important notions in logical systems
 A logical system L is complete iff
 || L  implies  |
(i.e., all valid formulas are provable)
 A logical system L is sound iff
 | implies  || L 
(i.e., no invalid formula is provable)
 Second order logics
Links for the young researcher
AI-MAS Links of interest
Academic publishing
Writing a Scientific Paper
ISI Web of Knowledge
Master Journal List
Conference Proceedings Citation Index
TED – Ideas worth spreading