CS 2710, ISSP 2610

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CS 2710, ISSP 2610

• Chapter 10, Part 1
• Knowledge Representation

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KR

• Last 3 chapters syntax, semantics, and proof
  theory of propositional and first-order logic
• Chapter 10 what content to put into an agents
  KB
• How to represent knowledge of the world

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Natural Kinds

• Some categories have strict definitions
  (triangles, squares, etc)
• Natural kinds dont
• Define a cup (distinguishing it from bowls, mugs,
  glasses, etc)
• Bachelor is the Pope a bachelor?
• But logical treatment can be useful (can extend
  with typicality, uncertainty, fuzziness)

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Upper Ontologies

• An ontology is similar to a dictionary but with
  greater detail and structure
• Ontology concepts, relations, axioms that
  formalize a field of interest
• Upper ontology only concepts that are meta,
  generic, abstract cover a broad range of domain
  areas
• IEEE Standard Upper Ontology Working Group

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Anything AbstractObjects
GeneralizedEvents Sets Numbers
RepresentationalObjects Interval Places
PhysicalObjects Processes
Categories Sentences Measurements
Moments things stuff
times weights
animals agents solid liquid gas
Lower concepts are specializations of their
parents
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Categories and Objects

• I want to marry a Swedish woman
• Category of Swedish woman?
• A particular woman who is Swedish?
• Choices for representing categories predicates
  or reified objects
• basketball(b) vs member(b,basketballs)
• Lets go with the reified version

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Facts about categories and objects in FOL

• An object is a member of a category
• A category is a subclass of another category
• All members of a category have some properties
  (necessary properties)
• Members of a category can be recognized by some
  properties (sufficient properties)
• A category as a whole has some properties
• Note idealization of real categories
• Examples in Lecture

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Other Relationships

• disjoint (no members in common)
• exhaustive decomposition of a category (all
  members are in at least one of the sets)
• Partition disjoint, exhaustive decomposition
• Examples in lecture

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Composite Objects

• partof(england,europe)
• All X,Y,Z ((partof(X,Y) partof(Y,Z)) ?
  partof(X,Z))
• Heavy(bunchOf(apple1,apple2,apple3))
• Before continuing inspiration for creative
  reification!
• From Through the Looking Glass

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Measures

• Diameter(basketball12) inches(9.5)
• All XY ((member(X,dimestore) sells(X,Y)) ?
  cost(Y) (1))
• member(db1,dollarbills)
• member(db2,dollarbills)
• denomination(db1) (1)
• denomination(db2) (1)
• There are multiple dollar bills, but a single (1)

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Ordinal Comparisons

• But often scales are not so precisely defined
• Often, ordinal comparisons among members of
  categories are useful
• member(p1,poems) member(p2,poems) beauty(p1)
  lt beauty(p2)
• We dont have to say p1 has beauty 54.321
• Qualitative physics reasoning about physical
  systems without detailed equations and numerical
  simulations.

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Stuff versus Things

• Suppose some ice cream and a cat in front of you.
  There is one cat, but no obvious number of
  ice-cream things in front of you.
• A piece of an ice-cream thing is an ice-cream
  thing (until you get down to very low level)
• A piece of a cat is not a cat

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Stuff versus Things

• Linguistically distinguished, in English through
  mass versus count noun phrases
• a cat
• an ice-cream (you have to coerce this to a
  thing, such as an ice-cream bar, or a variety of
  ice cream)
• a sand, an energy
• some cat (you have to coerce this to a
  substance eeewww)
• Lecture representation schemes

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Actions, Situations, and EventsThe Situation
Calculus

• The robot is in the kitchen.
• in(robot,kitchen)
• He walks into the living room.
• in(robot,livingRoom)
• in(robot,kitchen,202pm)
• in(robot,livingRoom,217pm)
• But what if you are not sure when it was?
• We can do something simpler than rely on time
  stamps

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Situation Calculus Ontology

• Actions terms, such as forward and
  turn(right))
• Situations terms initial situation, say s0,
  and all situations that are generated by applying
  an action to a situation. result(a,s) names the
  situation resulting when action a is done in
  situation s.

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Situation Calculus Ontology continued

• Fluents functions and predicates that vary from
  one situation to the next. By convention, the
  situation is the last argument of the fluent.
  holding(robot,gold,s0)
• Atemporal or eternal predicates and functions do
  not change from situation to situation.
  gold(g1). lastName(wumpus,smith).
  adjacent(livingRoom,kitchen).

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Sequences of Actions

• Also useful to reason about action sequences
• All S resultSeq(,S) S
• All A,Se,S resultSeq(ASe,S)
  resultSeq(Se,result(A,S))
• resultSeq(a,b,a2,a3,so) is
• result(a3,result(a2,result(b,result(a,s0)

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Modified Wumpus World

• Wont worry about agents orientation
• Fluent predicates at(O,X,S) and holding(O,S)
• Initial situation at(agent,1,1,s0)
  at(g1,1,2,s0)
• But we want to exclude possibilities from the
  initial situation too

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Initial KB

• All O,X (at(O,X,s0) ?? (Oagent X 1,1) v
  (Og1 X 1,2))
• All O holding(O,s0)
• Eternals
• gold(g1) adjacent(1,1,1,2)
  adjacent(1,2,1,1).

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Goal g1 is in 1,1

• At(g1,1,1,resultSeq(
• go(1,1,1,2),grab(g1),go(1,2,1,1),s0)
• Planning by answering the query
• Exists S at(g1,1,1,resultSeq(S,s0))
• So, what has to go in the KB for such queries to
  be answered?...

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Possibility and Effect Axioms

• Possibility axioms
• Preconditions ? poss(A,S)
• Effect axioms
• poss(A,S) ? changes that result from that action

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Axioms for our Wumpus World

• For brevity we will omit universal quantifies
  that range over entire sentence. S ranges over
  situations, A ranges over actions, O over objects
  (including agents), G over gold, and X,Y,Z over
  locations.

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Possibility Axioms

• The possibility axioms that an agent can
• go between adjacent locations,
• grab a piece of gold in the current location, and
  
• release gold it is holding

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Effect Axioms

• If an action is possible, then certain fluents
  will hold in the situation that results from
  executing the action
• Going from X to Y results in being at Y
• Grabbing the gold results in holding the gold
• Releasing the gold results in not holding it

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Frame Problem

• We run into the frame problem
• Effect axioms say what changes, but dont say
  what stays the same
• A real problem, because (in a non-toy domain),
  each action affects only a tiny fraction of all
  fluents

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Frame Problem (continued)

• One solution approach is writing explicit frame
  axioms, such as
• At(O,X,S) (Oagent) holding(O,S) ?
  at(O,X,result(Go(Y,Z),S))
• With F fluent predicates and A actions, need
  O(AF) frame axioms
• But if an action has at most E effects, then need
  only O(AE).