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Logic for Knowledge Representation: Categories, Relationships, and Actions

Explore how logic, categories, and actions are used in knowledge-based agents. Represent categories as predicates or objects, and understand relationships between categories like disjoint categories and partitions. Learn about physical composition, measurements, substances, and objects. Discover the challenges of representing beliefs, uncertain information, and dynamic information. Dive into Situation Calculus, Frame Problem, and Event Calculus.

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Logic for Knowledge Representation: Categories, Relationships, and Actions

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  1. Knowledge Representation CS 171/271 (Chapter 10) Some text and images in these slides were drawn fromRussel & Norvig’s published material

  2. Using Logic forKnowledge Representation • Propositional and First-Order Logic describe the technology for knowledge-based agents • What gets into these knowledge bases? • Categories, objects, substances • Agent actions, situations, events • Beliefs • Uncertain information • Dynamic information

  3. Categories • Representing categories • As predicates: Singer( Madonna) • As objects: Member( Madonna, Singers ) or Madonna  Singers • Related notions • Subclasses/subcategories (  ) • Categories versus properties • Categories of categories

  4. Relationships between Categories • Disjoint categories • Disjoint( {Animals, Vegetables} ) • Exhaustive decomposition • ExhaustiveDecomposition( {Faculty,Staff,Administrators}, UniversityPersonnel ) • Partition • Partition( {Males,Females}, Persons )

  5. Physical Composition • Part-of relationship • Composite objects • With structural properties (e.g., car as something with wheels and other things attached to it) • Bunches (e.g., apples in a bag)

  6. Measurements • Measures as objects • Measure: a number with units • Example • Length(L1) = Inches(1.5)

  7. Substances and Objects • World not necessarily individuated • Not always divided into distinct objects • In the English language • Count nouns versus mass nouns • Has special properties • Example:x  Butter  PartOf( y,x )  y  Butter

  8. Actions • In the context of an agent, we need to represent actions and consequences • Need to aslo worry about percepts, time, changing situations, and many others • Situation calculus or event calculus

  9. Situation Calculus • Situations • Objects/terms that stand for the states between actions carried out (initial situation and generated situations after an action) • Result( a, s ) names the resulting state when action a is executed in situation s • Fluents • Predicates/functions that vary across situations • Eternal predicates • Not dependent on situation

  10. Actions in Situation Calculus • Possibility Axiom • preconditions  Poss( action, situation ) • Example:“can move to a square if it is adjacent” • Effect Axiom • Poss( action, situation )  changes • Example:“moving updates agent position”

  11. Frame Problem • In the real world, most things stay the same from one situation to the next • Change occurs for a tiny fraction of the fluents • Note: effect action would often only note those changes • Frame problem: problem of representing those that stay the same • Efficiency/compactness issue • Representational versus Inferential

  12. Event Calculus • Time as objects • Fluents hold at points in time • Reasoning can be made over time intervals

  13. Other Challenges • Beliefs • Uncertain Information • Dynamic Information • Read Chapter 10

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