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Knowledge Representation & Reasoning Lecture #1

Knowledge Representation & Reasoning Lecture #1. UIUC CS 498: Section EA Professor: Eyal Amir Fall Semester 2005. Explicit Knowledge Representation. What is knowledge? What applications do you know of knowledge? Where do we not need knowledge? How do we use knowledge?. Examples.

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Knowledge Representation & Reasoning Lecture #1

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  1. Knowledge Representation & ReasoningLecture #1 UIUC CS 498: Section EAProfessor: Eyal Amir Fall Semester 2005

  2. Explicit Knowledge Representation • What is knowledge? • What applications do you know of knowledge? • Where do we not need knowledge? • How do we use knowledge?

  3. Examples

  4. Knowledge in Different Forms • CYC, OpenMind, SUMO – Commonsense • Ontologies – frame-based, semantic web • Medical knowledge • Diseases/symptoms networks • Dynamic systems • Specific applications: NLP, Databases

  5. Knowledge Representation and Reasoning (KR&R) • Advice taker: a paradigm for KR&R • Represent knowledge (with statements) • Add statements when you want to give advice (control knowledge = statements) • World vs Reasoner (Decision Maker) Actions/Decisions Reasoner + Knowledge World Sensory information

  6. Knowledge Representation and Reasoning (KR&R) • Advice taker: a paradigm for KR&R • Examples: • A robot moving and manipulating the world • An internet agent booking flights for us • A virtual agent in a computer game Actions/Decisions Reasoner + Knowledge World Sensory information

  7. Reasoning Tasks • A robot moving and manipulating the world • Track the environment and its body (actions) • Update its knowledge with new information (sensors & communications) • Make timely decisions • Safe decisions • Take uncertainty into account • Learning and generalizing from knowledge

  8. Reasoning Algorithm Actions/Decisions World KB Tasks Mngr Sensory information Symbols to Sensors Example • A robot moving and manipulating the world Reasoner + Knowledge

  9. Reasoning Algorithm KB Tasks Mngr Symbols to Sensors Example Details 1 • A robot moving and manipulating the world Reasoning Algorithm Task: Decide on action Call reasoning algorithm with query. Examples: - next_action(move_fwd) - next_action(look_door) KB Tasks Mngr Symbols to Sensors

  10. Example Details 2 • A robot moving and manipulating the world Reasoning Algorithm Task: Is the action safe? Call reasoning algorithm with query. Examples: - safe_action(move_fwd) - safe_action(look_door,s) KB Tasks Mngr Symbols to Sensors

  11. Example Details 3 • A robot moving and manipulating the world Reasoning Algorithm Task: Track the world Use reasoning to update knowledge. Examples: get_KB(result(move_fwd)) get_KB(result(arm(10),s)) KB Tasks Mngr Symbols to Sensors

  12. Example Use of Reasoning 1 • Task: select an action to perform • Logical KB: (a) Prove that KB entails move_fwd (e.g.,FOL) (b) Find a model of KB that satisfies move_fwd (e.g., propositional logic) • Probabilistic KB: • Find the probability of move_fwd (e.g., BNs) • Find an action that gives best utility (MDPs)

  13. Example Use of Reasoning 2 • Task: find cause of error Err • Logical KB: Abduction: Find an explanation Exp such that KB  Exp logically entails Err • Probabilistic KB: • Find the set of variable assignments that has maximum posterior probability given Err

  14. Knowledge Representation and Reasoning (KR&R) • Two agents interacting • Sales and purchase agent • Collaboration to achieve a task • Information agent and user agent Request Reasoning Agent 1 + Knowledge Base 1 Agent 2 + Knowledge Base 2 Response

  15. Knowledge Representation and Reasoning (KR&R) • Query answering: • Formal verification of digital circuits • Temporal verification of programs • Prediction and explanation Query Human / Software Reasoning with A Knowledge Base Answer

  16. Tractability of Reasoning • More expressive languages require more time to reason with Expressivity – Tractability tradeoff • Compact representations not always more efficient for reasoning • Reasoning with a complete model many times easier than reasoning with general knowledge in the same language

  17. Summary: Why, When, How KR&R • Reasoning with knowledge is good when we are not sure about knowledge or query. • The language of KB is determined by the application: • Need for expressive language • Need for fast/accurate response • Knowledge is entered by hand or learned • Tasks for reasoning algorithms vary

  18. In This Course: Representation • Knowledge Representation Languages • Logic: propositional, First-Order Logic, Description Logics [, defaults, linear logic] • Probabilities: graphical models (e.g., BNs), relational-probabilistic models [, causality] • Specific cases: • Dynamic worlds: logical, probabilistic • Space/Shape: logical, probabilistic • Knowledge about knowledge

  19. In This Course: Reasoning • Exact inference: • Fundamental principles • Structure: treewidth [, context-based] • Approximate inference: • Sampling, variational, lower/upper bounds,… • Special tasks: • Dynamic worlds: filtering, smoothing,… • Space/Shape: logical, probabilistic • Equality

  20. Course Requirements • You should have seen: • Probability & Statistics (e.g., Normal distr., Bayes rule, axioms of probability) • Propositional Logic (e.g., CNF, SAT, de-Morgan, logical equivalence, entailment) • Can catch up using the books for the class or [Russell & Norvig ’03] • Computational complexity (level of CS473)

  21. Course Requirements #2 • Mathematical maturity: proofs, understanding • Independence: follow beyond your presentation reading to gain depth • Independence: project will require readings that are not specified • Independence: search for information instead of thinking it will come to you

  22. Reading Materials • Required: • [BL ’04] Brachman, Levesque, Knowledge Representation and Reasoning, 2004. • [CDLS ’99] Cowell, Dawid, Lauritzen, and Speigelhalter, Probabilistic Networks and Expert Systems, 1999. • See website for more information: http://reason.cs.uiuc.edu/eyal/classes/f05/cs498ea

  23. (Group) Project Choice • Two possible projects (done in one group): • Semantic Web: build semantic description of websites using a probabilistic extension to OWL + applying distributed reasoning algorithms • Mapping people’s location in Siebel Center using cameras, knowledge, and inference • 12th lec. (Oct 4): Project proposals (~3-pages) • 24th lec. (Nov 15): Progress Review (~1 page) • Final Exam (Dec 16): Projects due

  24. Cheating Policy • First offense: • Exam: zero on exam • Project/homework: zero + loss of full letter grade • Second offense: • In same course: failure • In different course: expulsion

  25. More Administrativia • Late HW submission policy: 7 days • Date/time for midterm ? • Course grading • Newsgroup

  26. Next • Example of (non-traditional) reasoning with first-order logic in a robotics setting • Reminder of Propositional Logic notation and concepts

  27. Propositional Logic • Language includes • Prop. symbols • Logical connectives • Formulas: • Atom • Literal • Formula • KB: Set of formulas

  28. Representing Knowledge • Propositional symbols represent facts under consideration: • there_is_rain, there_are_clouds, door1_open, robot_in_pos_56_210 • Not propositions: • is_there_rain? • location_of_robot • Dan_Roth

  29. Representing Knowledge • Knowledge bases are sets of formulae • There_is_rain  there_are_clouds • Robot_in_pos_3_1  Position_3_1_empty • Has_drink  coffee  tea

  30. Knowledge Engineering • Select a language: set of features • Examine cases • Decide on dependencies between features • Write dependencies formally • Test

  31. Propositional Logic • Semantics: • Truth assignments that satisfy KB/formula I1 I2 I3 I4 Interpretations: I1[a]=FALSE I1[b]=FALSE assign truth values to propositional symbols

  32. -a -b a -b -a b a b Propositional Logic • Semantics: • Truth assignments that satisfy KB/formula I1 ╨ M1 I2 M1= I3 M2= I4 Models of f: Interpretations that satisfy f

  33. ╨ ╨ ╨ ╨ Propositional Logic • Semantics: • Truth assignments that satisfy KB/formula Logical Entailment ╨ M1

  34. ┴ Propositional Logic • Semantics: • Truth assignments that satisfy KB/formula Logical Entailment ╨ Deduction (inference)

  35. More Notations • Interpretations ~ Models • Axioms – formulae that are “assumed” • Signature – the symbols used by a KB • Theory ~ KB (a set of axioms), or • Theory ~ the complete set of sentences entailed by the axioms • Sentence = formula (in prop. logic)

  36. More Notations • The value that symbol p takes in model M: • [[ M ]] p • pM • M[p] -- we will primarily use this • Clauses: {lit1, lit2, lit3,…} or lit1 lit2 lit3...

  37. Summary • Propositional logic as a language for representing knowledge • Did not touch on reasoning procedures • Defined language, signature, models

  38. Homework • Read readings for next time (on website) • Homework #0

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