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What do you mean, “What do I mean?” continued. Lecture 10-1 November 30 th , 1999 CS250. Steps in Building. Decide what to talk about Decide on a vocabulary Encode general rules Encode an instance Pose queries. General Ontologies. Categories Measures Composite Objects

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    1. What do you mean, “What do I mean?” continued... Lecture 10-1 November 30th, 1999 CS250 CS250: Intro to AI/Lisp

    2. Steps in Building • Decide what to talk about • Decide on a vocabulary • Encode general rules • Encode an instance • Pose queries CS250: Intro to AI/Lisp

    3. General Ontologies • Categories • Measures • Composite Objects • Time, Space and Change • Events and Processes • Physical Objects • Substances • Mental Objects and Beliefs CS250: Intro to AI/Lisp

    4. Categories • Categories • Reification • How many people live on Earth? • Inheritance • Creating taxonomies • Kentucky Fried Chicken • Dewey decimal • LoC • MeSh CS250: Intro to AI/Lisp

    5. Measures • Examples: Height, mass, cost • Measure = Units function + a Number CS250: Intro to AI/Lisp

    6. Composite Objects • Not inheritance • Difference between subclass and member • Schema • Script CS250: Intro to AI/Lisp

    7. Composite Objects • Not inheritance • Difference between subclass and member • General event descriptions • Schema • Script CS250: Intro to AI/Lisp

    8. Using Events to Represent Change • What’s the problem? • Continuous time • Multiple agents • Actions of different durations • Event calculus - Reify events CS250: Intro to AI/Lisp

    9. Event Calculus Vocabulary • Events are splotches in the space-time continuum • Events have subevents • Some events are intervals CS250: Intro to AI/Lisp

    10. Examples • Suppose we wish to represent facts about market manias f fBulbEating  SubEvent(f,TulipMania)  PartOf(Location(f), Holland) s sStockFrenzy  SubEvent(s,USBullMarket)  PartOf(Location(f), ??) s sStockFrenzy  SubEvent(s,USBullMarket)  TradedOn(Exchange(s), NASDAQ) CS250: Intro to AI/Lisp

    11. Place • How are places like intervals? • Relation In holds among places • Location function: Maps an object to the smallest place that contains it CS250: Intro to AI/Lisp

    12. Kurt D. Fenstermacher: Sonnenfeld directed: Men in Black (1997) Get Shorty (1995) The Addams Family (1991) Processes • Why do we need processes when we have events? • How can we say: • Barry Sonnenfeld was flying some time yesterday • Barry was flying all day yesterday E(Flying(Barry), Yesterday) T(Flying(Barry), Yesterday) CS250: Intro to AI/Lisp

    13. A Logical Blender Suppose Bill is accused of killing a zucchini, and when the cold, but efficient, Detective Frigerator (known to his pals as simply “Re”) questions the orange juice pitcher in FOPL, the orange juice has no idea how to say: “Bill was in the kitchen with the tomato all day yesterday” CS250: Intro to AI/Lisp

    14. Composite Events • Use And to combine two events with the usual semantics: And isn’t so bad, but disjunction is a bit more complicated -- how do we say: “I saw the whole thing, the beef or the broccoli stabbed the zucchini all afternoon.”  p,q,e T(And(p, q), e)  T(p, e)  T(q, e) CS250: Intro to AI/Lisp

    15. Time & Intervals • Time is pretty important • Divvy up time into: Moments and ExtendedIntervals • Define a couple handy functions Start End Time Date CS250: Intro to AI/Lisp

    16. When Intervals Get Together • Meet • Before • After • During • Overlap CS250: Intro to AI/Lisp

    17. Objects in the Space-Time Continuum • Remember that events are splotches of space-time • Some events have coherence through time • Need to capture the idea of an object existing through time CS250: Intro to AI/Lisp

    18. Roman Empire • Roman Empire spread across much of Eurasia, expanding and contracting, from 753 B.C. until the 5th century A.D. CS250: Intro to AI/Lisp

    19. Roman Empire at 218 B.C. CS250: Intro to AI/Lisp

    20. Roman Empire at 117 A.D. CS250: Intro to AI/Lisp

    21. Roman Empire at 395 A.D. CS250: Intro to AI/Lisp

    22. Fluents • Roman Empire is an event • Subevents include • First, Second and Third Punic Wars • One of the first known hammer and anvil movements in battle (216 BC @ Cannae) • A fluent allows us to capture the notion of the Roman Empire throughout time T(In(Gaul, Roman Empire), AD12) T(Male(Emperor(RomanEmpire)), 1stCenturyAD) CS250: Intro to AI/Lisp

    23. Fluent Flavors • Fluent is a function, f:Situations Fvalues • Domain is the set of all situations (states of the world) If Fvalues is {TRUE, FALSE} then it’s a Propositional fluent If Fvalues is {All situations} then it’s a Situational fluent CS250: Intro to AI/Lisp

    24. Substances • Less vs. fewer • Intrinsic vs. extrinsic properties • Substances are those things that are fungible CS250: Intro to AI/Lisp

    25. Going, Like, Totally Mental • What are other agents know, and what are they thinking? • “Everybody’s looking at me” • “They’re trying to kill me” • “You look like someone who knows where I can find extra virgin olive oil” • Start with a Believes predicate Believes(Agent, x) CS250: Intro to AI/Lisp

    26. Reification & You • A good first pass: • Treat Flies(Superman) as a propositional fluent • Relationships like Believes,Know and When between agents and propositions are propositional attitudes • The problem: Can Clark fly? Believes(Agent, Flies(Superman)) CS250: Intro to AI/Lisp

    27. “It is clear.” • Referential transparency • Any term can be substituted for an equal term • FOL is referentially transparent CS250: Intro to AI/Lisp

    28. Knowing for Action • Knowing preconditions: What do you need to know to do action a? • Knowledge effects: What effect does performing action a have on an agent’s knowledge? CS250: Intro to AI/Lisp

    29. Replacing that Zucchini • Grocery shopping • Percepts • Actions • Goals • Environment CS250: Intro to AI/Lisp

    30. You say you wanna resolution? CS250: Intro to AI/Lisp

    31. Chain of Fools American(x)  • Forward chaining • Start with sentences, apply SdMP (GMP) to derive new conclusions • Good when adding new facts • Backward chaining • Start from sentences and derive premises • Got goal? CS250: Intro to AI/Lisp

    32. Forward Chaining for each rule that p unifies with a premise if the other premises are known then add conclusion to KB keep on chainin’ • Renaming • Two sentences are renamings of one another if they are the same except for variable names CS250: Intro to AI/Lisp

    33. Composition • Define COMPOSE(T1, T2) to apply two substitutions in a row: SUBST(COMPOSE(T1, T2), p) = SUBST(T2, SUBST(T1, p)) CS250: Intro to AI/Lisp

    34. Forward Chaining in Action 1) American(x)  Weapon(y)  Nation(z)  Hostile(z)  Sells(x, y, z)  Criminal(x) 2) Owns(Nono, x)  Missile(x)  Sells(West, Nono, x) 3) Missile(x)  Weapon(x) 4) Enemy(x, America) Hostile(x) ForwardChain(KB, American(West)) ForwardChain(KB, Nation(Nono)) ForwardChain(KB, Enemy(Nono, America)) ForwardChain(KB, Hostile(Nono)) ForwardChain(KB, Owns(Nono, M1)) ForwardChain(KB, Missile(M1)) ForwardChain(KB, Sells(West, Nono, M1)) ForwardChain(KB, Weapon(M1)) ForwardChain(KB, Criminal(West)) CS250: Intro to AI/Lisp

    35. What’s the Problem? • Will-nilly inferencing CS250: Intro to AI/Lisp

    36. Backward Chaining • Start from what you’re trying to prove, and look for support • When a query q is asked: If a matching fact q’ is known return the unifier for each rule whose consequent q’ matches q attempt to prove each premise of rule by backward chaining CS250: Intro to AI/Lisp

    37. Revisiting Unification • Can we unify: Knows(John, x) & Knows(x, Elizabeth) CS250: Intro to AI/Lisp

    38. Now what’s wrong? • Is this complete? • Inference procedure i is complete iff KB |=i whenever KB |=  PhD(x)  HighlyQualified(x) PhD(x)  EarlyEarnings(x) HighlyQualified(x)  Rich(x) EarlEarnings(x)  Rich(x) CS250: Intro to AI/Lisp

    39. Does a Complete Algorithm Exist? • Kurt says yes • Any sentence that is entailed by another set of sentences can be proved from that set • In other words: We can find a complete inference procedure • What is it? CS250: Intro to AI/Lisp

    40.   ,         ,       Resolution • Remember Chapter 6? • Is this an improvement? CS250: Intro to AI/Lisp

    41. Resolution Procedure • Resolution is a refutation procedure: To prove KB |= , show KB   is unsatisfiable CS250: Intro to AI/Lisp

    42. Resolution Procedure CS250: Intro to AI/Lisp

    43. Canonical Forms • CNF • Start with a bunch of disjunctions • Pretend all of them are joined with one big conjunct • INF • Each sentence is an implication with a conjunction of atoms on the left, and a disjunction of atoms on the right CS250: Intro to AI/Lisp

    44. Out of the Frying Pan? • Created GMP, needed Horn clauses • But can’t always transform sentences into Horn clauses! • Find another procedure • Stumble upon resolution, which needs CNF or INF • Can we always transform into CNF or INF? CS250: Intro to AI/Lisp

    45. CNF vs. Horn • The diff • In Horn, RHS must be an atom • In CNF, RHS is a disjunction • MP can derive atomic conclusions, what about resolution? • Recast terms as implications of TRUE CS250: Intro to AI/Lisp

    46. Conversion to CNF • Can convert any FOL KB into CNF CS250: Intro to AI/Lisp

    47. Skolemization • Remove existential quantifiers by elimination • Like EE, but more general • Replace existentially quantified variables with unique constants • What happens if there’s a universal quantification hiding inside? • Example: Everyone has a heart CS250: Intro to AI/Lisp

    48. Resolution Proof • To prove : • Negate it,  • Convert it to CNF • Add to a CNF KB • Infer a contradiction CS250: Intro to AI/Lisp

    49. Da Proof CS250: Intro to AI/Lisp