1 Knowledge Representation CS 171/CS 271

2 How to represent reality? Use an ontology (a formal representation of reality) General/abstract domain Specific domains Goal is to incorporate an ontology in a computer system such that the system seems to know the domain

3 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

4 Categories Intelligent system -> a system that seems to “reason” Human reasoning is based largely on categories Presence of a certain object from perceptual input Category membership inferred from perceived properties Predictions can be made about that said object

5 Categories Example: You observe the presence of a certain something (perceptual input) Green, mottled skin, large size, ovoid shape (perceived properties from perceptual input) Conclusion: that something is a Watermelon Watermelon is a fruit Prediction? Watermelon is good for fruit salad

6 Categories Example: You observe the presence of a certain something (perceptual input) Average height, brown skin, familiar hair, Dardar shape (perceived properties from perceptual input) Conclusion: that something is Dardar Dardar is a friend Dardar is a good choice to ask food from

7 Categories Test: Is there a difference between property and category?

8 Categories Representing categories As predicates: Singer( Madonna) As objects: Member( Madonna, Singers ) or Madonna  Singers

9 Categories Basketball(b) Member(b,Basketball) b  Basketball Subset(Basketballs, Balls) Balls  Basketballs

10 Categories A category being a set of its members A complex object that has Member and Subset relations defined to it

11 Categories To simplify the knowledge base, inheritance may be used whenever applicable Inheritance in objects involving categories Think of inheritance in object oriented programing What examples of inheritance can you think of?

12 Categories Related notions Subclasses/subcategories (  ) Categories versus properties Categories of categories

13 Relationships between Categories Disjoint categories Exhaustive decomposition Partition

14 Relationships between Categories Disjoint categories No members in common Exhaustive decomposition If not a member of one, must be a member of the other Partition A disjoint exhaustive decomposition

15 Relationships between Categories Disjoint categories Disjoint( {Animals, Vegetables} ) Exhaustive decomposition ExhaustiveDecomposition( {Faculty,Staff,Administrators}, UniversityPersonnel ) Partition Partition( {Males,Females}, Persons ) Look at the white board

16 Physical Composition Part-of relationship Composite objects With structural properties (e.g., car as something with wheels and other things attached to it) Transitive and Reflexive Look at the white board

17 Physical Composition “The apples in the bag weigh 2 pounds” Weight of 2 pounds ascribed to a set of apples – is this the correct way? Set is an abstract mathematical concept with elements, but not weight Concept of the BUNCH

18 Physical Composition BunchOf( {Apple1, Apple2, Apple3} ) BunchOf(Apples) BunchOf(Apples) vs. Apples

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

20 Measurements Diamater(Basketball) = Inches(9.5) LastPrice(Basketball) = $(19) d  Days -> Duration(d) = Hours(24)

21 Measurements Inches(0) vs. Centimeters(0) vs. Seconds(0) Note differences in what they represent

22 Measurements Measures are easy if they are quantitative How about qualitative measurements? Assign quantities to qualitative concepts? Is this the correct/best way?

23 Measurements Quantifying non numerical measures Unnecessary! Imagine imposing a numerical scale on beauty An important aspect of measures is not the particular numerical values but the fact that the measures can be ordered What does this mean?

24 Substances and Objects x  Butter  PartOf( y,x )  y  Butter This is true x  Dog  PartOf( y,x )  y  Dog Is this true?

25 Substances and Objects Slice butter in 2, you get 2 tangible objects, both are butter Slice a dog in 2, what do you get? Illustrates 2 important concepts: STUFF THING

26 Substances and Objects World not necessarily individuated Not always divided into distinct objects In the English language Count nouns versus mass nouns

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

28 Situation Calculus Situations Fluents Eternal Predicates

29 Situation Calculus Situations Logical terms consisting of the initial situation S 0 and all situations generated by applying an action to a situation 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

30 Situation Calculus Fluents Predicates/functions that vary across situations Holding(G1, S 0 ) Age( Dardar, S 3 )

31 Actions in Situation Calculus Possibility Axiom It is possible to execute an action Effect Axiom What happens when a possible action is executed

32 Actions in Situation Calculus Possibility Axiom preconditions  Poss( action, situation ) Example: “can move to a square if it is adjacent” “can feed Dardar if Dardar is hungry” Effect Axiom Poss( action, situation )  changes Example: “moving updates agent position” “Feeding Dardar makes Dardar not hungry”

33 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

34 Inadequacy of Situation Calculus Situation Calculus works well with Single agent involved Actions are discrete What if: Not dealing with a single agent Actions have duretion and may overlap across situations

35 Event Calculus Based on points in time instead of situations Time as objects Fluents hold at points in time Reasoning can be made over time intervals (more humanlike!) More next week

36 Other Challenges Beliefs Uncertain Information Dynamic Information