What do you mean What do I mean

What do you mean, “What do I mean? ” continued. . . Lecture 10 -1 November 30 th, 1999 CS 250 Lecture 10 -1 CS 250: 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 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Categories • Reification – How many people live on Earth? • Inheritance • Creating taxonomies – Kentucky Fried Chicken – Dewey decimal – Lo. C – Me. Sh Lecture 10 -1 CS 250: Intro to AI/Lisp

Measures • Examples: Height, mass, cost • Measure = Units function + a Number Lecture 10 -1 CS 250: Intro to AI/Lisp

Composite Objects • Not inheritance – Difference between subclass and member • Schema • Script Lecture 10 -1 CS 250: Intro to AI/Lisp

Composite Objects • Not inheritance – Difference between subclass and member • General event descriptions – Schema – Script Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Event Calculus Vocabulary • Events are splotches in the space-time continuum • Events have subevents • Some events are intervals Lecture 10 -1 CS 250: Intro to AI/Lisp

Examples • Suppose we wish to represent facts about market manias f f Bulb. Eating Sub. Event(f, Tulip. Mania) Part. Of(Location(f), Holland) s s Stock. Frenzy Sub. Event(s, USBull. Market) Part. Of(Location(f), ? ? ) s s Stock. Frenzy Sub. Event(s, USBull. Market) Traded. On(Exchange(s), NASDAQ) Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

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 E(Flying(Barry), Yesterday) – Barry was flying all day yesterday T(Flying(Barry), Yesterday) Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Composite Events • Use And to combine two events with the usual semantics: p, q, e T(And(p, q), e) T(p, e) T(q, e) 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. ” Lecture 10 -1 CS 250: Intro to AI/Lisp

Time & Intervals • Time is pretty important – Divvy up time into: Moments and Extended. Intervals – Define a couple handy functions Start End Time Date Lecture 10 -1 CS 250: Intro to AI/Lisp

When Intervals Get Together • • • Meet Before After During Overlap Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Roman Empire • Roman Empire spread across much of Eurasia, expanding and contracting, from 753 B. C. until the 5 th century A. D. Lecture 10 -1 CS 250: Intro to AI/Lisp

Roman Empire at 218 B. C. Lecture 10 -1 CS 250: Intro to AI/Lisp

Roman Empire at 117 A. D. Lecture 10 -1 CS 250: Intro to AI/Lisp

Roman Empire at 395 A. D. Lecture 10 -1 CS 250: 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 BC @ Cannae) • A fluent allows us to capture the notion of the Roman Empire throughout time T(In(Gaul, Roman Empire), AD 12) T(Male(Emperor(Roman. Empire)), 1 st. Century. AD) Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Substances • Less vs. fewer • Intrinsic vs. extrinsic properties • Substances are those things that are fungible Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Reification & You • A good first pass: Believes(Agent, Flies(Superman)) • 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? Lecture 10 -1 CS 250: Intro to AI/Lisp

“It is clear. ” • Referential transparency – Any term can be substituted for an equal term – FOL is referentially transparent Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Replacing that Zucchini • Grocery shopping – Percepts – Actions – Goals – Environment Lecture 10 -1 CS 250: Intro to AI/Lisp

You say you wanna resolution? Lecture 10 -1 CS 250: Intro to AI/Lisp

Chain of Fools American(x) • Forward chaining – Start with sentences, apply Sd. MP (GMP) to derive new conclusions – Good when adding new facts • Backward chaining – Start from sentences and derive premises – Got goal? Lecture 10 -1 CS 250: Intro to AI/Lisp

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 Lecture 10 -1 CS 250: Intro to AI/Lisp

Composition • Define COMPOSE(T 1, T 2) to apply two substitutions in a row: SUBST(COMPOSE(T 1, T 2), p) = SUBST(T 2, SUBST(T 1, p)) Lecture 10 -1 CS 250: 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) Forward. Chain(KB, American(West)) Forward. Chain(KB, Nation(Nono)) Forward. Chain(KB, Enemy(Nono, America)) Forward. Chain(KB, Hostile(Nono)) Forward. Chain(KB, Owns(Nono, M 1)) Forward. Chain(KB, Missile(M 1)) Forward. Chain(KB, Sells(West, Nono, M 1)) Forward. Chain(KB, Weapon(M 1)) Forward. Chain(KB, Criminal(West)) Lecture 10 -1 CS 250: Intro to AI/Lisp

What’s the Problem? • Will-nilly inferencing Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Revisiting Unification • Can we unify: Knows(John, x) & Knows(x, Elizabeth) Lecture 10 -1 CS 250: Intro to AI/Lisp

Now what’s wrong? • Is this complete? • Inference procedure i is complete iff KB |=i whenever KB |= Ph. D(x) Highly. Qualified(x) Ph. D(x) Early. Earnings(x) Highly. Qualified(x) Rich(x) Earl. Earnings(x) Rich(x) Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Resolution • Remember Chapter 6? , • Is this an improvement? Lecture 10 -1 CS 250: Intro to AI/Lisp

Resolution Procedure • Resolution is a refutation procedure: To prove KB |= , show KB is unsatisfiable Lecture 10 -1 CS 250: Intro to AI/Lisp

Resolution Procedure Lecture 10 -1 CS 250: 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 -1 CS 250: 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 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Conversion to CNF • Can convert any FOL KB into CNF Lecture 10 -1 CS 250: 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 -1 CS 250: Intro to AI/Lisp

Resolution Proof • To prove : – Negate it, – Convert it to CNF – Add to a CNF KB – Infer a contradiction Lecture 10 -1 CS 250: Intro to AI/Lisp

Da Proof Lecture 10 -1 CS 250: Intro to AI/Lisp