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

Using Logic for Knowledge 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

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

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

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)

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

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

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

Situation Calculus Situations Fluents Eternal predicates 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

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”

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

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

Other Challenges Beliefs Uncertain Information Dynamic Information Read Chapter 10