Transcript Slides - AI-MAS

Master of Science in Artificial Intelligence, 2010-2012
Knowledge Representation
and Reasoning
University "Politehnica" of Bucharest
Department of Computer Science
Fall 2010
Adina Magda Florea
http://turing.cs.pub.ro/krr_10
curs.cs.pub.ro
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 different
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
area
Grading
 Course grades
Mid-term exam
Final exam
Projects
Laboratory
20%
30%
30%
20%
 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
Syllabus
1. General knowledge representation issues
Readings:
http://plato.stanford.edu/entries/logic-ai/
2. Logical agents – Logical knowledge representation and
reasoning
• First order predicate logic revisited, ATP – Lect. 2
Readings:
AIMA Chapter 7 http://aima.cs.berkeley.edu/newchap07.pdf
• Nonmonotonic logics and reasoning – Lect. 3
Readings:
Non-monotonic Logic, Stanford Encyclopedia of Philosophy
http://plato.stanford.edu/entries/logic-nonmonotonic/
Nonmonotonic Reasoning, G. Brewka, I. Niemela, M. Truszczynski
http://www.informatik.uni-leipzig.de/~brewka/papers/NMchapter.pdf
Nonmonotonic Reasoning With WebBased Social Networks
http://www.mindswap.org/~katz/papers/socialnet-defaults.pdf
Syllabus
• Modal logic, logics of knowledge and beliefs – Lect 4
Readings: Modal logic on Wikipedia
http://en.wikipedia.org/wiki/Modal_logic
+ to be announced
• Semantic networks and description logics, reasoning
services – Lect 5
Readings: to be announced
• Knowledge representation for the Semantic Web –
Lect. 6
Readings:
Ontology knowledge representation - from description logic to OWL
Description Logics as Ontology Languages for the Semantic Web
http://lat.inf.tu-dresden.de/research/papers/2005/BaSaJS60.pdf
Syllabus
Midterm exam (written examination) – 1h
3. Rule based agents
• Rete: Efficient unification – Lect. 7
Readings:
The RETE algorithm
http://www.cis.temple.edu/~ingargio/cis587/readings/rete.html
• The Soar model, universal subgoaling and chunking –
Lect. 8, 9
Readings:
A gentle introduction to Soar, an architecture for human cognition
http://ai.eecs.umich.edu/soar/sitemaker/docs/misc/GentleIntroduction-2006.pdf
• Modern rule based systems – Lect. 10, 11
Syllabus
4. Probabilistic agents
• Probabilistic knowledge representation and reasoning
– Lect. 12
Readings:
to be announced
5. Intelligence without representation and reasoning
vs. Strong AI – Lect. 14
(one lecture – invited professor)
Final exam
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
representation 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
components:
• the representation's fundamental
conception of intelligent reasoning;
• the set of inferences the representation
sanctions;
• 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
accomplished.
• 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
world.
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
representations
 Symbolic representations of propositions
or statements that are believed by some
agent.
What is Reasoning?
 Not interested (in this 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 http://plato.stanford.edu/entries/logicalconsequence/
 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 +
semantics
 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
premises.
Logical consequence (entailment)
 Model centered approach to logical
consequence
 Models are abstract mathematical structures that
provide possible interpretations for each of the
non-logical objects 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.)
Model centered approach
 Interpretation of a formula
 Model of a formula
 Entailment or logical consequence
 A formula F is a logical consequence of a set of
formulas P1,…Pn iff F is true in all interpretations in
which P1,…Pn are true.
 P1,… Pn || L F
 T Formula F is a logical consequence of a set of
formulas P1,…Pn iff P1,…Pn F is valid.
 T Formula F is a logical consequence of a set of
formulas P1,…Pn iff P1…  Pn  ~F is inconsistent.
Proof centered approach
 Theorem, deduction
 Formal system
 Inference rule
S =< A, F , A ,  >
R 
R
R  F n  F , y =  y1 ,..., y n   x, x, yi  F , i = 1, n
 Premise set
 = {y1 ,..., yn }
E1 = E0 U{x| y  E0n , y  x}
n 1
 Consequence of 
Ei (i  0)
E0 =   A
E2 = E1 U{x| y  E1n , y  x}
n 1
Proof centered approach
 If E0 =   A then x  Ei is deductible from 
 |S x
 Theorems - the elements of Ei if E0 = A ( = )
x  Ei
 Demonstration
| R x
Proof approach important notions
 Th() – set of provable theorems in 
• Monotonicity
• 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 inference
 Th() – the least fixed point of this closure
process
Properties of logical systems
Important properties of logical systems:
 Consistency - no theorem of the system contradicts
another.
 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.
Properties of 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)
 FOPL
 Second order logics
Links for the young researcher

AI-MAS Links of interest
http://aimas.cs.pub.ro/links

Academic publishing
http://en.wikipedia.org/wiki/Academic_publishing

Writing a Scientific Paper
http://www.oup.com/us/samplechapters/0841234620/?view=usa

ISI Web of Knowledge
http://isiwebofknowledge.com/

Master Journal List
http://science.thomsonreuters.com/mjl/

Conference Proceedings Citation Index
http://wokinfo.com/products_tools/multidisciplinary/webofscience/cpci/

TED – Ideas worth spreading
http://www.ted.com/