1. Lectures on Artificial Intelligence – CS289 Conceptual Graphs
18th September 2006
Dr Bogdan L. Vrusias

2. Contents Definition of Conceptual Graphs Basic building blocks
Concept node representation
Exercise
18th September 2006
Bogdan L. Vrusias © 2006

3. 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.
18th September 2006
Bogdan L. Vrusias © 2006

4. 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
18th September 2006
Bogdan L. Vrusias © 2006

5. Conceptual Graphs: Basic Structure
("The cat sat on the mat")
Rules for assembling percepts
Words
Percepts
Grammar Rules
CAT
STAT
SIT
LOC
MAT
PS: percepts are fragments of images that fit together like pieces of a jigsaw puzzle
18th September 2006
Bogdan L. Vrusias © 2006

6. Conceptual Graphs: Basic Structure
Alternative notation for text based representation:
[cat] --> (stat) --> [sit] --> (loc) --> [mat]
Square brackets denote concept nodes.
Parentheses denote relation nodes.
18th September 2006
Bogdan L. Vrusias © 2006

7. 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
18th September 2006
Bogdan L. Vrusias © 2006

8. Perception
‘Perception is the process of building a working model that represents and interprets sensory input’.
The reception of sensory input, ‘a mosaic of percepts’, is converted into concepts:
Concrete concepts – that have associated percepts
Abstract concepts – that do not have any associated percepts.
18th September 2006
Bogdan L. Vrusias © 2006

9. 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.
18th September 2006
Bogdan L. Vrusias © 2006

10. Conceptual Graphs Example
Consider the sentence: "A cat sitting on a mat"
This sentence can be interpreted at different levels:
There are concrete concepts: cat, mat and sitting which enable us to experience the external word and motor mechanism to react to it.
The words of our natural language, arranged in accordance with the grammar of the language, is one way of articulating and disseminating the experience.
18th September 2006
Bogdan L. Vrusias © 2006

11. Conceptual Graphs Example
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
Animal – Posture – Furniture
Living Being – Act – Household Object
A hierarchy of concept type defines the relationship between concepts at different levels of generality
Increasing Abstraction
18th September 2006
Bogdan L. Vrusias © 2006

12. Conceptual Graphs Example
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.
18th September 2006
Bogdan L. Vrusias © 2006

13. Conceptual Graphs Example
The above sentence relates to an episode or to some context to which it is relevant.
Each episode may have some deeper mental associations, like emotions.
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.
18th September 2006
Bogdan L. Vrusias © 2006

14. 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
18th September 2006
Bogdan L. Vrusias © 2006

15. Example Consider the sentence:
Mary gave John the boring book authored by Tom & Jerry
There are three main parts: (1), (2), and (3)
(1)
(2)
(3)
18th September 2006
Bogdan L. Vrusias © 2006

16. Example agent Person: Mary give recipient Person: John
(1): Mary gave John the boring book authored by Tom & Jerry
agent
Person: Mary
give
recipient
Person: John
Both relation nodes have two arcs each and are referred to as expressing a 2-ary or binary relation between the two concepts
18th September 2006
Bogdan L. Vrusias © 2006

17. Example
(2): Mary gave John the boring book authored by Tom & Jerry
boring
book
The relation node has only one arc and thus refers to a 1-ary or unary relation
18th September 2006
Bogdan L. Vrusias © 2006

18. Example Person: Tom author book Person: Jerry
(3): Mary gave John the boring book authored by Tom & Jerry
Person: Tom
author
book
Person: Jerry
The relation node has 3-arcs and is referred to as expressing 3-ary or ternary relation
18th September 2006
Bogdan L. Vrusias © 2006

19. Formal Conceptual Relations
Entity:*x
Entity*y
accompaniment (ACCM)
attribute (ATTR)
characteristic (CHRC)
content (CONT)
part (PART)
possession (POSS)
support (SUPP)
Event(Act)
Attribute
manner (MANR)
18th September 2006
Bogdan L. Vrusias © 2006

20. Formal Conceptual Relations
Event(Act)
Entity
result (RSLT)
source (SOUR)
Entity (Animate)
agent (AGNT)
recipient (RCPT)
Entity (Place)
destination (DEST)
path (PATH)
Entity (Substance)
material (MATR)
Function
Data
argument (ARG)
State*x
State*y
causation (CAUS)
18th September 2006
Bogdan L. Vrusias © 2006

21. Concept Nodes
Recall that in the discussion of Collins and Quillian’s semantic networks, we have found that these networks were logically inadequate!
This situation was not resolved in some of the subsequent formulations of semantic networks. Specifically, it was difficult in a typical semantic network notation to distinguish between nodes describing:
classes and subclasses
classes and members
18th September 2006
Bogdan L. Vrusias © 2006

22. Concept Nodes In the sentence:
Tom is a cat, a feline mammal
Tom is_a cat is_a feline is_a mammal
individual species subclass class
The relation "is_a" is used to describe relationships between concepts that are mildly different.
18th September 2006
Bogdan L. Vrusias © 2006

23. Concept Nodes
A good representation should allow us to distinguish between:
Individuals and species
Species and classes
Classes and subclasses
Individuals may have properties that may not influence their belonging to a subclass:
Tom is a brown tabby
Should not influence the observation that:
A tabby cat is a kind of cat
18th September 2006
Bogdan L. Vrusias © 2006

24. Concept Nodes
In CG theory, 'every concept is a unique individual of a particular type'.
Concept nodes are labelled with descriptors or names like "dog", "cat", "gravity", etc. The labels refer to the class or type of individual represented by the node.
Each concept node is used to refer to an individual concept or a generic concept.
In CG theory we have a relation called: name
18th September 2006
Bogdan L. Vrusias © 2006

25. Concept Nodes colour cat: "Tom" brown
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
colour
cat: "Tom"
brown
18th September 2006
Bogdan L. Vrusias © 2006

26. Concept Nodes: Unnamed Individuals
Consider the example that we do not know the name of a cat that is brown:
Each concept node in a CG may be used to represent specific but unnamed individuals by a unique prescribed number.
colour
cat: #12345
brown
18th September 2006
Bogdan L. Vrusias © 2006

27. Concept Nodes: Multiple Names
We subsequently found out that the cat is called by different names: "Sylvester", "Sugar Pie" and "Squidgy Bod":
name
"Sylvester"
name
cat: #12345
"Sugar Pie"
name
"Squidgy Bod"
18th September 2006
Bogdan L. Vrusias © 2006

28. Concept Nodes: Unspecified Individuals
General markers can also be used to refer to an unspecified individual. The CG:
Refers to an unspecified cat. Notationally, unspecified individuals are shown by the existence of an asterisk ("*")
BUT… this is usually omitted (cat = cat:*).
colour
cat
brown
colour
cat: *
brown
18th September 2006
Bogdan L. Vrusias © 2006

29. 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.
agent
object
dog:*X
scratch
ear
instrument
part
part
paw
dog:*X
18th September 2006
Bogdan L. Vrusias © 2006

30. Canonical Graphs
A conceptual graph is a combination of concept nodes and relation nodes where every arc of every conceptual relation is linked to a concept. This could lead sometimes to sensible statements like
"a bunny sitting on a mat"
and at time will lead to nonsense like:
"colourless green ideas sleep furiously"
Sowa distinguishes the nonsensical graphs from those that represent real or possible situations in the external world by declaring the later as canonical.
Certain conceptual graphs are canonical. New graphs may become canonical or be canonised by perception, formation rules, or through "insight".
18th September 2006
Bogdan L. Vrusias © 2006

31. Exercises
Please create the conceptual graph of the following sentence:
John is between a rock and a hard place
18th September 2006
Bogdan L. Vrusias © 2006

32. Solution 1 rock between person: John place attribute hard
"John is between a rock and a hard place"
rock
between
person: John
place
attribute
hard
18th September 2006
Bogdan L. Vrusias © 2006

33. Closing Questions??? Remarks??? Comments!!! Evaluation!
18th September 2006
Bogdan L. Vrusias © 2006