Transcript Artificial Intelligence

AI – CS364
Knowledge Representation
Introduction to Conceptual Graphs
19th September 2006
Dr Bogdan L. Vrusias
[email protected]
AI – CS364
Knowledge Representation
Contents
•
•
•
•
Definition of Conceptual Graphs
Basic building blocks
Concept node representation
Exercise
19th September 2006
Bogdan L. Vrusias © 2006
2
AI – CS364
Knowledge Representation
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.
19th September 2006
Bogdan L. Vrusias © 2006
3
AI – CS364
Knowledge Representation
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
19th September 2006
Bogdan L. Vrusias © 2006
4
AI – CS364
Knowledge Representation
Conceptual Graphs: Basic Structure
("The cat sat on the mat")
Rules for assembling
percepts
Words
Percepts
CAT
Grammar Rules
STAT
SIT
LOC
MAT
PS: percepts are fragments of images that fit together like pieces of a jigsaw puzzle
19th September 2006
Bogdan L. Vrusias © 2006
5
AI – CS364
Knowledge Representation
Conceptual Graphs: Basic Structure
• Alternative notation for text based representation:
[cat] --> (stat) --> [sit] --> (loc) --> [mat]
• Square brackets denote concept nodes.
• Parentheses denote relation nodes.
19th September 2006
Bogdan L. Vrusias © 2006
6
AI – CS364
Knowledge Representation
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
19th September 2006
Bogdan L. Vrusias © 2006
7
AI – CS364
Knowledge Representation
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.
19th September 2006
Bogdan L. Vrusias © 2006
8
AI – CS364
Knowledge Representation
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.
19th September 2006
Bogdan L. Vrusias © 2006
9
AI – CS364
Knowledge Representation
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.
19th September 2006
Bogdan L. Vrusias © 2006
10
AI – CS364
Knowledge Representation
Conceptual Graphs Example
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
Animal – Posture – Furniture
Living Being – Act – Household Object
Increasing
Abstraction
A hierarchy of concept type defines the relationship between concepts at
different levels of generality
19th September 2006
Bogdan L. Vrusias © 2006
11
AI – CS364
Knowledge Representation
Conceptual Graphs Example
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.
19th September 2006
Bogdan L. Vrusias © 2006
12
AI – CS364
Knowledge Representation
Conceptual Graphs Example
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.
19th September 2006
Bogdan L. Vrusias © 2006
13
AI – CS364
Knowledge Representation
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
19th September 2006
Bogdan L. Vrusias © 2006
14
AI – CS364
Knowledge Representation
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)
19th September 2006
Bogdan L. Vrusias © 2006
15
AI – CS364
Knowledge Representation
Example
(1): Mary gave John the boring book authored by Tom & Jerry
Person: Mary
agent
Person: John
recipient
give
Both relation nodes have two arcs each and are referred to as expressing a 2ary or binary relation between the two concepts
19th September 2006
Bogdan L. Vrusias © 2006
16
AI – CS364
Knowledge Representation
Example
(2): Mary gave John the boring book authored by Tom & Jerry
book
boring
The relation node has only one arc and thus refers to a 1-ary or unary relation
19th September 2006
Bogdan L. Vrusias © 2006
17
AI – CS364
Knowledge Representation
Example
(3): Mary gave John the boring book authored by Tom & Jerry
Person: Tom
book
author
Person: Jerry
The relation node has 3-arcs and is referred to as expressing 3-ary or ternary
relation
19th September 2006
Bogdan L. Vrusias © 2006
18
AI – CS364
Knowledge Representation
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)
19th September 2006
Attribute
manner (MANR)
Bogdan L. Vrusias © 2006
19
AI – CS364
Knowledge Representation
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)
19th September 2006
Bogdan L. Vrusias © 2006
20
AI – CS364
Knowledge Representation
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
19th September 2006
Bogdan L. Vrusias © 2006
21
AI – CS364
Knowledge Representation
Concept Nodes
• In the sentence:
– Tom is a cat, a feline mammal
Tomis_a
individual
cat
is_a
species
feline
is_a
mammal
subclass
class
• The relation "is_a" is used to describe relationships between concepts
that are mildly different.
19th September 2006
Bogdan L. Vrusias © 2006
22
AI – CS364
Knowledge Representation
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
19th September 2006
Bogdan L. Vrusias © 2006
23
AI – CS364
Knowledge Representation
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
19th September 2006
Bogdan L. Vrusias © 2006
24
AI – CS364
Knowledge Representation
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"
19th September 2006
colour
Bogdan L. Vrusias © 2006
brown
25
AI – CS364
Knowledge Representation
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.
19th September 2006
Bogdan L. Vrusias © 2006
26
AI – CS364
Knowledge Representation
Concept Nodes: Multiple Names
• We subsequently found out that the cat is called by different names:
"Sylvester", "Sugar Pie" and "Squidgy Bod":
cat: #12345
19th September 2006
name
"Sylvester"
name
"Sugar Pie"
name
"Squidgy Bod"
Bogdan L. Vrusias © 2006
27
AI – CS364
Knowledge Representation
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:*).
19th September 2006
Bogdan L. Vrusias © 2006
28
AI – CS364
Knowledge Representation
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
instrument
paw
19th September 2006
Bogdan L. Vrusias © 2006
ear
part
part
dog:*X
29
AI – CS364
Knowledge Representation
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".
19th September 2006
Bogdan L. Vrusias © 2006
30
AI – CS364
Knowledge Representation
Exercises
• Please create the conceptual graph of the following
sentence:
– John is between a rock and a hard place
19th September 2006
Bogdan L. Vrusias © 2006
31
AI – CS364
Knowledge Representation
Solution 1
• "John is between a rock and a hard place"
rock
person: John
between
place
attribute
19th September 2006
Bogdan L. Vrusias © 2006
hard
32
AI – CS364
Knowledge Representation
Closing
•
•
•
•
Questions???
Remarks???
Comments!!!
Evaluation!
19th September 2006
Bogdan L. Vrusias © 2006
33