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Knowledge Representation and Reasoning

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Title: Knowledge Representation and Reasoning


1
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

2
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

3
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

4
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.

5
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

6
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

7
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

8
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

9
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

10
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/

11
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

12
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?

13
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.

14
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?

15
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.

16
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.

17
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.

18
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/

19
5. Models of KRR
  • Symbolic logic and ATP
  • Probabilistic
  • Temporal
  • Rules
  • Structured

20
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.

21
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.

22
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.)

23
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.

24
6.3 Proof centered approach
  • Theorem, deduction
  • Formal system
  • Inference rule
  • Premise set
  • Consequence of ?

25
Proof centered approach
  • If then is deductible from
    ?
  • ? ?S x
  • Theorems - the elements of Ei if
  • Demonstration ? R x
  •  

26
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

27
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.

28
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

29
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 ?

30
  • 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
31
First order logic
32
8. Automated Reasoning
33

34
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?

35
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36
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39
  • 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
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