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Knowledge Representation

Knowledge Representation. CPSC 386 Artificial Intelligence Ellen Walker Hiram College. What we know…. Knowledge can be represented using first-order predicate logic Several inference algorithms are useful Forward Chaining Backward Chaining Resolution (All use unification).

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Knowledge Representation

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  1. Knowledge Representation CPSC 386 Artificial Intelligence Ellen Walker Hiram College

  2. What we know… • Knowledge can be represented using first-order predicate logic • Several inference algorithms are useful • Forward Chaining • Backward Chaining • Resolution • (All use unification)

  3. What we’ve ignored so far • Objects in the world tend to be related to each other • Classes, superclasses & subclasses • Part / whole hierarchies • Properties are inherited across relationships • The state of the world can change over time • Explicit representation of time • Frame axiom • Non-monotonic reasoning • We must reason without complete knowledge Closed world assumption • Not all knowledge is “black & white” (Ch 11) • Uncertainty • Statistics, fuzzy logic

  4. Classes • “I want to buy a basketball” • I want to buy BB27341 (NO) • I want to buy an object that is a member of the basketball class (YES) • Objects organized into a hierarchy by class • BB27341  basketballs • Basketballs  balls • Facts (objects) & rules (classes) • All balls are round. • All basketballs are <size> in diameter. • BB27341 is red, white and blue. • BB27341 is a basketball. • (Therefore BB27341 is round and <size> in diameter).

  5. Inheritance • If a property is true of a class, it is true of all subclasses of that class • If a property is true of a class, it is true of all objects that are members of that class • (If a property is true of a class, it is true of all objects that are members of subclasses of that class) • There are exceptions (to be dealt with later…)

  6. Part / Whole Inheritance • A cow has 4 legs • Each leg is part of the cow • The cow is in the field. • All of the cow’s parts are also in the field • The cow is (entirely) brown • All of the cow’s parts are brown • The cow is happy • All of the cow’s parts are happy (?) • Lesson: some properties are inherited by parts, others are not. This is generally made explicit by rules, such as • part-of(x,y) and location(y,z) -> location(x,z)

  7. Stuff vs. things • Some objects are “stuff” • When you divide the object, its parts are still the same: e.g. butter, snow • “stuff” cannot be referred to with “a” or “an” • “Please pass a butter” (?) • Other objects are “things” • When you divide them, you destroy them, e.g. aardvark, snowflake • “A snowflake landed on my nose” vs. “A snow landed on my nose”

  8. Situations and Events • A state of the world is a “situation” • Divide predicates into “eternal” and “fluent” • At(x,y,S) is fluent - S is the situation where it holds • Gold(g) is eternal - it is true in all situations • Each action causes a result • Result(move-to(x,y),Si) = At(x,y, Si+1)

  9. The Frame Problem • What about everything else? • Result(move-to(x,y), Si) = At(x,y, Si+1) and • z, z≠x at(z,w, Si)  at(z,w, Si+1) • This is a frame axiom • Representing all frame axioms explicitly is a pain • Instead: assume it’s the same if we’re not told it’s different • Fluent is true in new situation iff last action made it true, or if it was true in the previous situation • Real world example: what color is Obie’s hair? • We assume it hasn’t changed, but maybe she colored it today!

  10. Semantic Networks • Semantic networks are essentially a generalization of inheritance hierarchies • Each node is an object or class • Each link is a relationship • IS-A (the usual subclass or element relationship) • HAS-PART or PART-OF • Any other relationship that makes sense in context • Note: semantic networks predated OOP • Inheritance: follow one member-of link, as many subclass or other links as necessary. • Example: “Mary had a little lamb” (see board)

  11. Algorithm for Inheritance • If the current object has a value for the property, return that value • Otherwise, if the current object is a member of a class, return the value of the property of the class (recursively) • Otherwise, if the current object is a subclass, return the value of the property of the superclass (recursively) • This is depth-first search; stop at the first one found.

  12. Defaults and Exceptions • Exception for a single object: • Set a property of the object to the (exception) value • Default for a class • Set a property of the class to the (default) value • If there are multiple default values, the one “closest” to the object wins.

  13. Default & Exception example • All birds can fly. • Birds with broken wings are birds, but cannot fly. • Penguins are birds, but they cannot fly. • Magical penguins are penguins that can fly. • Who can fly? • Tweety is a bird. • Peter is a penguin. • Penelope is a magical penguin. • Note that beliefs can be changed as new information comes in that changes the classification of an object.

  14. Two Useful Assumptions • Closed World Assumption • Anything that I don’t know is true, I will assume to be false • (Negation as failure in Prolog) • Unique Names Assumption • Unique names refer to different objects • “Chris and the programmer …” implies Chris isn’t the programmer • Again, Prolog implements this assumption.

  15. NonMonotonic Logic • Once true (or false) does not mean always true (or false) • As information arrives, truth values can change (Penelope is a bird, penguin, magic penguin) • Implementations (you are not responsible for details) • Circumscription • Bird(x) and not abnormal(x) -> flies(x) • We can assume not abnormal(x) unless we know abnormal(x) • Default logic • “x is true given x does not conflict with anything we already know”

  16. Truth Maintenance Systems • These systems allow truth values to be changed during reasoning (belief revision) • When we retract a fact, we must also retract any other fact that was derived from it • Penelope is a bird. (can fly) • Penelope is a penguin. (cannot fly) • Penelope is magical. (can fly) • Retract (Penelope is magical). (cannot fly) • Retract (Penelope is a penguin). (can fly)

  17. Types of TMS • Justification based TMS • For each fact, track its justification (facts and rules from which it was derived) • When a fact is retracted, retract all facts that have justifications leading back to that fact, unless they have independent justifications. • Each sentece labeled IN or OUT • Assumption based TMS • Represent all possible states simultaneously • When a fact is retracted, change state sets • For each fact, use list of assumptions that make that fact true; each world state is a set of assumptions.

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