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

Lecture 10-1CS250: Intro to AI/Lisp Steps in Building Decide what to talk about Decide on a vocabulary Encode general rules Encode an instance Pose queries

Lecture 10-1CS250: Intro to AI/Lisp General Ontologies Categories Measures Composite Objects Time, Space and Change Events and Processes Physical Objects Substances Mental Objects and Beliefs

Lecture 10-1CS250: Intro to AI/Lisp Categories Reification –How many people live on Earth? Inheritance Creating taxonomies –Kentucky Fried Chicken –Dewey decimal –LoC –MeSh

Lecture 10-1CS250: Intro to AI/Lisp Measures Examples: Height, mass, cost Measure = Units function + a Number

Lecture 10-1CS250: Intro to AI/Lisp Composite Objects Not inheritance –Difference between subclass and member Schema Script

Lecture 10-1CS250: Intro to AI/Lisp Composite Objects Not inheritance –Difference between subclass and member General event descriptions –Schema –Script

Lecture 10-1CS250: Intro to AI/Lisp Using Events to Represent Change What’s the problem? –Continuous time –Multiple agents –Actions of different durations Event calculus - Reify events

Lecture 10-1CS250: Intro to AI/Lisp Event Calculus Vocabulary Events are splotches in the space-time continuum Events have subevents Some events are intervals

Lecture 10-1CS250: Intro to AI/Lisp 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)

Lecture 10-1CS250: Intro to AI/Lisp Place How are places like intervals? Relation In holds among places Location function: Maps an object to the smallest place that contains it

Lecture 10-1CS250: Intro to AI/Lisp 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 Kurt D. Fenstermacher: Sonnenfeld directed: Men in Black (1997) Get Shorty (1995) The Addams Family (1991) Kurt D. Fenstermacher: Sonnenfeld directed: Men in Black (1997) Get Shorty (1995) The Addams Family (1991) E(Flying(Barry), Yesterday) T(Flying(Barry), Yesterday)

Lecture 10-1CS250: Intro to AI/Lisp 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”

Lecture 10-1CS250: Intro to AI/Lisp 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)

Lecture 10-1CS250: Intro to AI/Lisp Time & Intervals Time is pretty important –Divvy up time into: Moments and ExtendedIntervals –Define a couple handy functions Start End Time Date

Lecture 10-1CS250: Intro to AI/Lisp When Intervals Get Together Meet Before After During Overlap

Lecture 10-1CS250: Intro to AI/Lisp 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

Lecture 10-1CS250: Intro to AI/Lisp Roman Empire Roman Empire spread across much of Eurasia, expanding and contracting, from 753 B.C. until the 5th century A.D.

Lecture 10-1CS250: Intro to AI/Lisp Roman Empire at 218 B.C.

Lecture 10-1CS250: Intro to AI/Lisp Roman Empire at 117 A.D.

Lecture 10-1CS250: Intro to AI/Lisp Roman Empire at 395 A.D.

Lecture 10-1CS250: Intro to AI/Lisp 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 Cannae) A fluent allows us to capture the notion of the Roman Empire throughout time T(Male(Emperor(RomanEmpire)), 1stCenturyAD) T(In(Gaul, Roman Empire), AD12)

Lecture 10-1CS250: Intro to AI/Lisp 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

Lecture 10-1CS250: Intro to AI/Lisp Substances Less vs. fewer Intrinsic vs. extrinsic properties Substances are those things that are fungible

Lecture 10-1CS250: Intro to AI/Lisp 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)

Lecture 10-1CS250: Intro to AI/Lisp 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))

Lecture 10-1CS250: Intro to AI/Lisp “It is clear.” Referential transparency –Any term can be substituted for an equal term –FOL is referentially transparent

Lecture 10-1CS250: Intro to AI/Lisp 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?

Lecture 10-1CS250: Intro to AI/Lisp Replacing that Zucchini Grocery shopping –Percepts –Actions –Goals –Environment

Lecture 10-1CS250: Intro to AI/Lisp You say you wanna resolution?

Lecture 10-1CS250: Intro to AI/Lisp Chain of Fools 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? American(x) 

Lecture 10-1CS250: Intro to AI/Lisp Forward Chaining Renaming –Two sentences are renamings of one another if they are the same except for variable names for each rule that p unifies with a premise if the other premises are known then add conclusion to KB keep on chainin’

Lecture 10-1CS250: Intro to AI/Lisp Composition Define COMPOSE(T1, T2) to apply two substitutions in a row: SUBST(COMPOSE(T1, T2), p) = SUBST(T2, SUBST(T1, p))

Lecture 10-1CS250: Intro to AI/Lisp 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))

Lecture 10-1CS250: Intro to AI/Lisp What’s the Problem? Will-nilly inferencing

Lecture 10-1CS250: Intro to AI/Lisp 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

Lecture 10-1CS250: Intro to AI/Lisp Revisiting Unification Can we unify: Knows(John, x) & Knows(x, Elizabeth)

Lecture 10-1CS250: Intro to AI/Lisp 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)

Lecture 10-1CS250: Intro to AI/Lisp 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?

Lecture 10-1CS250: Intro to AI/Lisp Resolution Remember Chapter 6?   ,         ,       Is this an improvement?

Lecture 10-1CS250: Intro to AI/Lisp Resolution Procedure Resolution is a refutation procedure: To prove KB |= , show KB   is unsatisfiable

Lecture 10-1CS250: Intro to AI/Lisp Resolution Procedure

Lecture 10-1CS250: Intro to AI/Lisp 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

Lecture 10-1CS250: Intro to AI/Lisp 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?

Lecture 10-1CS250: Intro to AI/Lisp 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

Lecture 10-1CS250: Intro to AI/Lisp Conversion to CNF Can convert any FOL KB into CNF

Lecture 10-1CS250: Intro to AI/Lisp 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

Lecture 10-1CS250: Intro to AI/Lisp Resolution Proof To prove  : –Negate it,  –Convert it to CNF –Add to a CNF KB –Infer a contradiction

Lecture 10-1CS250: Intro to AI/Lisp Da Proof