Artificial Intelligence Conceptual Graphs

LCWU
Knowledge Representation
Artificial Intelligence
Conceptual Graphs
LCWU
Contents
• Definition of Conceptual Graphs
• Basic building blocks
• Exercise
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LCWU
Definition of Conceptual Graphs

• John Sowa, formerly of IBM, is one of the key proponents of
conceptual graphs (CG). Sowa’s project is to create "a system of
logic for representing natural language semantics".
• Conceptual graphs form a knowledge representation language based on

the one hand in linguistics, psychology and philosophy, and data
structures and data processing techniques on the other.
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Definition of Conceptual Graphs

• The main aim is mapping perception onto an abstract representation
and reasoning system.
• A conceptual graph consists of concept nodes and relation nodes

– The concept nodes represent entities, attributes, states, and events
– The relation nodes show how the concepts are interconnected
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Conceptual Graphs: Basic Structure

("The cat sat on the mat")
Rules for assembling
Words
percepts
Percepts Grammar Rules
CAT STAT SIT LOC MAT
PS: percepts are fragments of images that fit together like pieces of a jigsaw puzzle
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Conceptual Graphs: Basic Structure

• Alternative notation for text based representation:
[cat] --> (stat) --> [sit] --> (loc) --> [mat]
• Square brackets denote concept nodes.
• Parentheses denote relation nodes.
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A Graph-Theoretic Definition
• Conceptual Graphs are finite, connected, bipartite graphs.
– Finite: because any graph (in 'human brain' or 'computer storage') can
only have a finite number of concepts and conceptual relations.
– Connected: because two parts that are not connected would simply be
called two conceptual graphs.
– Bipartite: because there are two different kinds of nodes: concepts and
conceptual relations, and every arc links a node of one kind to a node of
another kind
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Perception
• ‘Perception is the process of building a working model that represents
and interprets sensory input’.
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Perception
• For Sowa, a sensory icon is matched in an ideal brain to a single
percept or to a collection of percepts, which are combined to form a
complete image: an interconnected set of percepts.
• Percepts are combined in the brain and their interconnections stored as

a conceptual graph.
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Conceptual Graphs Example

• Consider the sentence: "A cat sitting on a mat"
• This sentence can be interpreted at different levels:
1. There are concrete concepts: cat, mat and sitting which enable us to
experience the external word and motor mechanism to react to it.
2. The words of our natural language, arranged in accordance with the

grammar of the language, is one way of articulating and disseminating
the experience.
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3. Each of the concepts in the sentence belongs to, or can be related
to, a category or class:
Animal>Cat; Furniture>Mat; Posture>Sit;

Living Being>Animal; Household Objects>Furniture; Act>Posture
Thus
Cat – Sit – Mat Increasing

Animal – Posture – Furniture Abstraction
Living Being – Act – Household Object
A hierarchy of concept type defines the relationship between concepts at

different levels of generality
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4. The concepts cat-sit-mat are related to each other in that:
– It is a common observation that some animate objects do sit on

certain concrete objects
– Even if we had never seen a cat sitting on a mat, we may derive the
conceptual graph on the basis of observation
– The order of the concrete concepts is important in that were we to

say that mat-sit-cat, it would be difficult to match this stated percept
with a conceptual graph in the ideal brain.
– Formation rules determine how each type of concept may be linked

to conceptual relations.
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5. The above sentence relates to an episode or to some context to
which it is relevant.
6. Each episode may have some deeper mental associations, like

emotions.
7. When we ask the question: what is the cat doing?, the answer is
that the cat is sitting and that its current location is the mat. The
cat’s STATe, its current ACTivity, its LOCation may each be
related to a procedure of some type.
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Conceptual Relations
• Concepts are linked by conceptual relations to form a conceptual
graph.
• If a conceptual relation has n-arcs, then it is said to be n-adic, and its

arcs are labelled 1, 2, …..n
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Example
• Consider the sentence:
– Mary gave John the boring book authored by Tom & Jerry
(1) (2) (3)
• There are three main parts: (1), (2), and (3)
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Example
(1): Mary gave John the boring book authored by Tom & Jerry
Person: Mary agent give
Person: John recipient
Both relation nodes have two arcs each and are referred to as expressing a 2-
ary or binary relation between the two concepts
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Example
book boring
The relation node has only one arc and thus refers to a 1-ary or unary relation
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Example
Person: Tom
book author
Person: Jerry
The relation node has 3-arcs and is referred to as expressing 3-ary or ternary
relation
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Formal Conceptual Relations
Concept 1 Concept 2 Relation

Entity:*x Entity*y accompaniment (ACCM)
attribute (ATTR)
characteristic (CHRC)
content (CONT)
part (PART)
possession (POSS)
support (SUPP)
Event(Act) Attribute manner (MANR)
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Formal Conceptual Relations
Concept 1 Concept 2 Relation

Event(Act) Entity result (RSLT)
source (SOUR)
Event(Act) Entity (Animate) agent (AGNT)
recipient (RCPT)
Event(Act) Entity (Place) destination (DEST)
path (PATH)
Entity (Substance) material (MATR)
Function Data argument (ARG)
State*x State*y causation (CAUS)
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Concept Nodes
• CG allows nodes to be labelled simultaneously with the name of the
individual the node represents and its type. The two are separated by a
colon (":")
• Consider the example:

– Tom, a cat, is brown
cat: "Tom" colour brown
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Concept Nodes: Unnamed Individuals

• Consider the example that we do not know the name of a cat that is
brown:
cat: #12345 colour brown
• Each concept node in a CG may be used to represent specific but

unnamed individuals by a unique prescribed number.
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Concept Nodes: Multiple Names

• We subsequently found out that the cat is called by different names:
"Sylvester", "Sugar Pie" and "Squidgy Bod":
name "Sylvester"
cat: #12345 name "Sugar Pie"
name "Squidgy Bod"
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Concept Nodes: Unspecified Individuals

• General markers can also be used to refer to an unspecified individual.
The CG:
cat colour brown
• Refers to an unspecified cat. Notationally, unspecified individuals are

shown by the existence of an asterisk ("*")
cat: * colour brown
• BUT… this is usually omitted (cat = cat:*).
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Concept Nodes: Named Variables

• Named variables can also be used to refer to an individual. These are
represented by an asterisk followed by the variable name.
• This is useful to indicate nodes that are the same unspecified

individual.
dog:*X agent scratch object ear
instrument part
paw part dog:*X

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Exercises
• Please create the conceptual graph of the following sentence:
– John is between a rock and a hard place
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Solution 1
• "John is between a rock and a hard place"
rock
person: John between
place
attribute hard
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LCWU

Definition of Conceptual Graphs

• Conceptual graphs form a knowledge representation language based on

Definition of Conceptual Graphs

• A conceptual graph consists of concept nodes and relation nodes

Conceptual Graphs: Basic Structure

CAT STAT SIT LOC MAT

Conceptual Graphs: Basic Structure

[cat] --> (stat) --> [sit] --> (loc) --> [mat]

• Square brackets denote concept nodes.

• Parentheses denote relation nodes.

• Percepts are combined in the brain and their interconnections stored as

Conceptual Graphs Example

• This sentence can be interpreted at different levels:

2. The words of our natural language, arranged in accordance with the

Conceptual Graphs Example

Animal>Cat; Furniture>Mat; Posture>Sit;

Cat – Sit – Mat Increasing

A hierarchy of concept type defines the relationship between concepts at

Conceptual Graphs Example

– It is a common observation that some animate objects do sit on

– The order of the concrete concepts is important in that were we to

– Formation rules determine how each type of concept may be linked

Conceptual Graphs Example

6. Each episode may have some deeper mental associations, like

• If a conceptual relation has n-arcs, then it is said to be n-adic, and its

(1) (2) (3)

• There are three main parts: (1), (2), and (3)

Person: Mary agent give

Person: John recipient

Formal Conceptual Relations

Concept 1 Concept 2 Relation

Formal Conceptual Relations

Concept 1 Concept 2 Relation

• Consider the example:

cat: "Tom" colour brown

Concept Nodes: Unnamed Individuals

cat: #12345 colour brown

• Each concept node in a CG may be used to represent specific but

Concept Nodes: Multiple Names

cat: #12345 name "Sugar Pie"

name "Squidgy Bod"

Concept Nodes: Unspecified Individuals

cat colour brown

• Refers to an unspecified cat. Notationally, unspecified individuals are

cat: * colour brown

• BUT… this is usually omitted (cat = cat:*).

Concept Nodes: Named Variables

• This is useful to indicate nodes that are the same unspecified

dog:*X agent scratch object ear

paw part dog:*X

– John is between a rock and a hard place

person: John between

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