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Knowledge Representation and Reasoning

Master of Science in Artificial Intelligence,

2012-2014

- University "Politehnica" of Bucharest
- Department of Computer Science
- Fall 2012
- Adina Magda Florea
- http//turing.cs.pub.ro/krr_11
- curs.cs.pub.ro

Lecture 1

- Lecture outline
- Course goals
- Grading
- Textbooks and readings
- Syllabus
- Why KR?
- KRR Challenges
- What is KRR?
- 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 KRR - Being able to complete a project in this research

area

Grading

- Course grades Mid-term exam 20

Final exam 30 Projects

30 Laboratory

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 (2010)

by Stuart Russell and Peter Norvig - Knowledge Representation and Reasoning by Ronald

Brachman and Hector Levesque, Morgan Kaufman,

2004 - 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
- Readings
- AIMA Chapter 7 http//aima.cs.berkeley.edu/newch

ap07.pdf - Nonmonotonic logics and reasoning
- Readings
- Non-monotonic Logic, Stanford Encyclopedia of

Philosophy http//plato.stanford.edu/entries/logi

c-nonmonotonic/ - Nonmonotonic Reasoning, G. Brewka, I. Niemela,

M. Truszczynski - http//www.informatik.uni-leipzig.de/brewka/pap

ers/NMchapter.pdf - Nonmonotonic Reasoning With WebBased Social

Networks - http//www.mindswap.org/katz/papers/socialnet-d

efaults.pdf

Syllabus

- Modal logic, logics of knowledge and beliefs
- Readings Modal logic on Wikipedia
- http//en.wikipedia.org/wiki/Modal_logic
- to be announced
- Semantic networks and description logics,

reasoning services - Readings to be announced
- Knowledge representation for the Semantic Web
- 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
- Readings
- The RETE algorithm
- http//www.cis.temple.edu/ingargio/cis587/readin

gs/rete.html - The Soar model, universal subgoaling and chunking

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
- Readings to be announced

Syllabus

- 4. Probabilistic agents
- Probabilistic knowledge representation and

reasoning - Readings to be announced
- 5. Temporal reasoning
- Readings to be announced
- 6. Reasoning with actions
- Planning
- Readings to be announced
- 7. Intelligence without representation and

reasoning vs. Strong AI - Calls Debate
- Final exam

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/?v

iewusa - ISI Web of Knowledge
- http//isiwebofknowledge.com/
- Master Journal List
- http//science.thomsonreuters.com/mjl/
- Conference Proceedings Citation Index
- http//wokinfo.com/products_tools/multidisciplinar

y/webofscience/cpci/ - TED Ideas worth spreading
- http//www.ted.com/

Lecture 1

- Readings for Lecture 1
- http//plato.stanford.edu/entries/logic-ai/
- Readings for Lecture 2
- AIMA Chapter 7 http//aima.cs.berkeley.edu/new

chap07.pdf

1. Why KR?

- We understand by "knowledge" all kinds of facts

about the world. - Knowledge is necessary for intelligent behavior

(human beings, robots). - In this course we consider representation of

knowledge and how we can use it in making

intelligent artifacts. - What is knowledge?

2. KRR Challenges

- Challenges of KRR
- 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.

3. 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. - Symbolic representations
- Non-symbolic representations
- Symbolic representations set of propositions or

statements that are believed by some agent.

4. What is Reasoning?

- Reasoning is the use of symbolic representations

of some statements in order to derive new ones. - Statements are abstract objects their

representations are concrete objects and can be

easily manipulated. - Reasoning should scale well we need efficient

reasoning algorithms - http//plato.stanford.edu/entries/logical-conseque

nce/

5. Models of KRR

- Symbolic logic and ATP
- Probabilistic
- Temporal
- Rules
- Structured

6. 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.

6.1 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

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.)

6.2 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.

6.3 Proof centered approach

- Theorem, deduction

- Formal system
- Inference rule
- Premise set
- Consequence of ?

Proof centered approach

- If then is deductible from

? - ? ?S x
- Theorems - the elements of Ei if
- 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

6.4 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

7. Logic based representations

- 2 possible aims
- to make the system function according to the

logic - to specify and validate the design
- Conceptualization of the world / problem
- Syntax - wffs
- Semantics - significance, model
- Model - the domain interpretation for which a

formula is true - Model - linear or structured
- M S ? - "? is true or satisfied in component S

of the structure M" - Model theory
- Generate new wffs that are necessarily true,

given that the old wffs are true - entailment KB

L ? - Proof theory
- Derive new wffs based on axioms and inference

rules KB -i ?

- PrL, FOPL

Linear model

Extend PrL, PL

Sentential logic of beliefs Uses beliefs atoms

BA(?) Index PL with agents

Situation calculus Adds states, actions

Symbol level

Modal logic Modal operators

Knowledge level

Structured models

Description Logics Subsumption relationships

Dynamic logic Modal operators for actions

Temporal logic Modal operators for time Linear

time Branching time

Logics of knowledge and belief Modal operators B

and K

CTL logic Branching time and action

BDI logic Adds agents, B, D, I

First order logic

8. Automated Reasoning

A logical puzzle

- Someone who lives in Dreadbury Mansion killed

Aunt Agatha. - Agatha, the butler, and Charles live in

Dreadbury Mansion, and are the only people who

live therein. - A killer always hates his victim, and is never

richer than his victim. - Charles hates no one that Aunt Agatha hates.
- Agatha hates everyone except the butler.
- The butler hates everyone not richer than Aunt

Agatha. - The butler hates everyone Aunt Agatha hates.
- No one hates everyone.
- Agatha is not the butler.
- Who killed Aunt Agatha?

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- Slides 35-38 are from the slides
- First-Order Theorem Proving
- Peter Baumgartner
- NICTA, Logic and Computation Program, Canberra
- Peter.Baumgartner_at_nicta.com.au