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CS 385 Fall 2006Chapter 7

Knowledge Representation

7.1.1, 7.1.5, 7.2

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Knowledge Representation

What do we have to represent what we know?– predicate calculus

– production systems

What other representations do we have?– mathematical objects (functions, matrices,...)

– data structures (CS 132)

– use-case diagrams (CS 310)

– ER diagrams (CS 325)

What more do we need?

Distinction between – the representational scheme (predicate calculus)

– the medium it is implemented in (PROLOG)

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Categories of Representational Schemes:

Logical: – predicate calculus with PROLOG to implement

– there are other logics

Procedural: – production system

– rule-based system (expert system, later)

Network: – nodes are objects, arcs are relations (a map)

Structured networks:– extensions to networks where each node is more complex

This chapter: the last two.

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Logic versus Association

Logical representations: – predicate calculus loses important real-world knowledge:

– person(X) → breathes(X) missing a lot of meaning

– OK to check grammar but not to interpret a sentence

Associations (semantic net): – the meaning of an object needs to be defined in terms of a network

of associations with other objects. lungs, oxygen,...

– this alternate to logic is used by psychologists and linguists to characterize the nature of human understanding

– an object is defined in terms of its associations with other objects

– inheritance hierarchy (canary isa bird, associate properties with each).

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Figure 6.1: Semantic network developed by Collins and Quillian in their research on human information storage and response times (Harmon and King 1985).

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Figure 6.2: Network representation of properties of snow and ice.

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7.1.5 Frames

Networks allow for some inheritance, but not effective aggregation

Networks can get big and messy

Frames: an object has named slots with– values

– procedures

– links to other frames

Slots – filled in as information becomes available

– loosely correspond to relations in a conceptual graph

Advantage: it is clearer the main object is a dog

Easier to indicate hierarchies via inheritance (from animal)

Accessories point to collar and bowl frames

Procedural info can be attached

e.g. how to calculate default values such as 4 legs.

e.g. deductions based on marital status, number of children,...

dog

superclass: animal

covering: fur

legs: 4

location:

accessories: collar, bowl

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Figure 6.12: Part of a frame description of a hotel room “Specialization” indicates a pointer to a superclass.

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7.3 Conceptual Graphs

A particular representation for semantic nets– finite, connected, bipartite

(2 types of nodes with vertices from 1 set to other) graphs

– nodes are concepts ( boxes) or conceptual relations (ellipses)

– each graph represents one concept

• a bird flies

• a dog has color brown

• a child has a parent that is mother and parent father.

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Labeling Concept Nodes

Concept node (box): can be labeled with type and referent.

Referent can be nothing, name, marker or variable:

dog

dog:fido

dog:#1232

dog:*X

• a dog barks

• fido barks

• a particular (unnamed) dog parks and bites

• a dog bit its owner

barks

barks

bites

barks

agent bites

objectdog:*X

personobject

agentowns

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Type Hierarchy

Lattice – a partial ordering on a set of types.

Equivalence relation: – reflexive: a = a

– symmetric: a = b → b = a

– transitive a = b and b = c → a = c

Order: – reflexive and transitive

– all elements are comparable

Partial order– some elements are comparable

– how would you relate human, student, parent, math student, cs student, anna, zahra, dog, fido

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┬ (universal type)

generalization human dog specialization

student parent

cs student

anna zahra fido

┴ (absurd type)

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Operations to Create New Graphs

copy: an exact copy

restrict: nodes replaced by a node representing their specialization

dog is a specialized animal

Note we lost information about dog

join: combines the two with the substitutions.

May have redundant info

simplify: removes it

animal eats

dog barks

dog eats

dog

barks

eats

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• loses the bone

• what if emma is a cat?

• what if the two dogs are not the same?

These are not sound inference

rules, but often good enough for

plausible, common sense

reasoning.

No guarantee the results are true

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7.2.5 Propositional Nodes

Defining relations between propositions:

dog:fido barks

person: mary knowexperiencer

object

proposition

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7.2.6 Conceptual Graphs and Logic

Rules:

1. Assign a variable to each generic concept: X ↔ dog

2. Assign a name to each individual concept: emma

3. Each concept node has a predicate with same name as in 2 and variables as in 1: dog(X). dog(emma)

4. Each n-ary conceptual relation (barks, bites) is an n-ary predicate whose name is the same as the relation and arguments correspond to the concept nodes linked to the relation

5. All variables are existentially quantified

dog

bites

barks

X (dog(X) barks(X) bites(X)

dog(emma) barks(emma) bites(emma)

dog: emma

bites

barks

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7.2.6 Conceptual Graphs and Logic

dog agent bites personobject

dog:*X agent1 bites

object2dog:*X

personobject1

agent2owns

X ↔ dog, Y ↔ bites, Z ↔ person

X, Y, Z (dog(X) agent(X,Y) bites(Y) object(Y, Z)

person(Z)

easier but not following the algorithm:

X, Y (dog(X) bites(X, Y) person(Y)

X, Y, Z, W (dog(X) agent1(X,Y) bites(Y) object1(Y, Z)

person(Z) agent2(Z,W) owns(W) object2(W,X)

X, Y (dog(X) person(Y) owns(Y,X) bites(X,Y)

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7.2.6 Conceptual Graphs and Logic

negation:

dog:fido barks

proposition

neg

dog barks

proposition

neg

fido does not bark

¬ (dog(fido) bark(fido) dog(fido) → ¬ bark(fido) bark(fido) → ¬ dog(fido)

dogs do not bark

X ¬ (dog(X) bark(X))