COMP4418 Knowledge Representation and Reasoning

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COMP4418 Knowledge Representation and Reasoning

• 2009 s2 - Introduction
• Michael Maher

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• Lectures 3-6pm, Mondays
• in Pioneer International Theatre,
• AGSM Building
• Course web page
• http//www.cse.unsw.edu.au/cs4418

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Assessment

• NO exams
• Frequent assignments
• at least every second week
• sometimes every week
• hard deadlines

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Academic Honesty

• Assignments must be all your own work
• Your work must not be available to others
• Severe consequences for plagiarism
• 0 for assignment
• F for COMP4418
• Expulsion from UNSW
• Death

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Course Structure

• Introduction
• Constraints
• Math. Programming
• Global Constraints
• Planning
• Satisfiability
• Belief Revision
• Mystery

• 20/7
• 20/7 - 17/8
• 24/8 - 31/8
• 14/9
• 21/9
• 28/9
• 12/10
• 19/10

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Lecturers

• Jinbo Huang jinbo.huang_at_nicta.com.au
• Michael Maher mmaher_at_cse.unsw.edu.au
• Maurice Pagnucco morri_at_cse.unsw.edu.au
• Jussi Rintanen jussi.rintanen_at_nicta.co
  m.au
• Andrew Verden andrew.verden_at_nicta.com.au
  
• Toby Walsh twalsh_at_cse.unsw.edu.au
• Lanbo Zheng lanbo.zhang_at_nicta.com.au

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Intelligent Behaviour

• If we want an agent to behave intelligently it
  must
• Understand (part of) the world
• Recognise consequences of its actions (and
  inactions)
• Organise its actions to achieve its goals
• Do this in an efficient manner

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Approaches to Modelling

• Symbolic
• Clearly defined semantics
• Transparent reasoning
• Meta-level reasoning supported

• Non-symbolic
• Closer to life
• Combination of reflexes
• Black box

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Symbolic approach

• Knowledge
• Representations
• Reasoning
• Dealing with (mostly) NP-hard problems
• Languages range from problem-specific to general
  purpose

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Knowledge

• Understanding of the world
• More than just data - relationships
• abstraction or generalization from data
• Restructuring of information
• emphasizes structure
• Belief is similar (same?)

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Knowledge

• Knowledge of many different things
• Objective/external
• sensorimotor
• affective
• Many different degrees of knowledge
• certain
• defeasible
• probabilistic

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Representation

• We use representations of the world and things in
  the world
• maps
• diagrams
• words
• numbers
• symbols
• Also mental representations

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Representation

• Generally we choose representations that support
• easy mapping to the world
• easy mapping from the world
• manipulations that correspond to actions in the
  world
• expressiveness
• efficiency

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Reasoning

• Reasoning is a process of making implicit
  knowledge explicit
• Generally it involves manipulating a
  representation according to rules
• Reasoning does not involve the meaning of the
  representation
• If the rules fit with the representation and the
  world then we can make guarantees about the
  conclusions

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KRR

• In general, we can use any syntax for our
  representations
• words, symbols, diagrams, data structures
• Often a restricted syntax is used for a specific
  purpose
• numerals for arithmetic
• map for travel

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KRR

• In this course we focus on logic as the basis for
  a representation language
• somewhat universal
• very well studied and understood
• many variants, extensions

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Logics

• In logic
• World is represented with constants, function
  symbols, predicate symbols
• Statements must follow fixed syntax
• Logical symbols (?,?,?, ) allow construction of
  composite statements
• Reasoning uses inference rules to manipulate
  statements

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Logics

• Given a set of statements, there are many
  possible worlds that satisfy all statements
• these are called models
• We often want reasoning to be sound, so that
  every conclusion holds for any of the possible
  worlds
• in particular, the world we are thinking of

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Logics

• We also prefer reasoning to be complete, so that
  every statement that holds in all possible worlds
  can be discovered by reasoning.
• this means that if reasoning cannot discover
  something about the world, it is because not
  enough information was given to begin with

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Logics

• We write T - p if p can be concluded by
  reasoning from T
• We write T p if p holds in every model of T
• Soundness if T - p then T p
• Completeness if T p then T - p

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Logics

• Reasoning
• deduction (finding consequences)
• abduction (finding causes)
• induction (knowledge from data)
• Abduction, induction generally not sound
• Deduction generally not complete

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Course Outline

• Introduction
• Constraints
• Satisfiability
• Planning
• Belief Revision
• Math. Programming

• Michael
• Michael, Andrew, Toby
• Jinbo
• Jussi
• Maurice
• Lanbo

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Constraints

• Flexible modelling and solving of combinatorial
  optimization problems
• Constraint solving
• algorithmic
• Constraint satisfaction
• pruning search
• Global constraints
• encapsulated algorithms for pruning
• Optimization
• Applications in many areas

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Boolean Satisfiability

• Prototypical NP-hard problem - SAT
• satisfiability of propositional clauses
• Many powerful systems
• Able to solve problems with 1,000,000s clauses,
  100,000s variables
• Target language for several KRR systems

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Mathematical Programming

• Linear Programming
• linear inequalities over real/rational numbers
• polynomial complexity
• Integer Programming
• linear inequalities over integers
• techniques based on linear programming
• NP-hard

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Planning

• Want to change the world to satisfy certain
  conditions - the goal
• Actions
• change the world, but
• have pre-conditions to apply
• A plan is a sequence of actions intended to
  achieve the goal
• Plans may need to cope with
• actions that fail
• sensors that are not accurate

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Belief Revision

• An agent has beliefs about the world
• New information may conflict with current beliefs
• more knowledge/facts about the world, or
• world changes
• How to update beliefs?
• retain new information
• lose as little of the old information
• Principles for performing these tasks
• Similarities to non-monotonic reasoning

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