Transcript Document

Knowledge Representation
Knowledge Representation
• Essential to artificial intelligence are
methods of representing knowledge. A
number of methods have been developed,
including:
– Logic : propositional and predicate logic
– Semantic Networks
– Conceptual Dependencies
– Scripts
– Frames
Representing Knowledge
with Logic
Logic systems began with Propositional Calculus in which declarative
statements with a truth value of true or false are represented by
P,Q,R, etc and combined with logic operators Or, And, Not, If. A
sentence such as “Bill must take CSC 2020” is represented by letter
P and is true or false. Propositional Calculus was extended to
Predicate Calculus by adding Predicates (relations), variables, and
quantifiers (For All and There Exists). A sentence such as “Every
CS major must take CSC 2020” is represented by “(For All X)(
CSMajor(X)  MustTake( CSC2020 ))” Given some facts
expressed in either Propositional or Predicate Calculus, new facts or
knowledge is inferred by inference rules such as modus ponens or
resolution. If the computer can find a path from given facts to a new
theorem, the path corresponds to a proof and finding such a path
constitutes an example of artificial intelligence
Propositional Logic
• A declarative statement such as “Bill is a CS student”
has a truth value of T or F and is denoted by P (a truth
variable)
• Propositions may be combined with logical operators
and the composite statement has value as shown below.
P  Q is true if either P or Q are true and false if both are false
P  Q is true if both P and Q are true and false if either is false.
¬ P is true if P is false and false if P is true
P  Q is true if P and Q have the same truth value and false if
their values differ
– P  Q is false if P is true and Q is false and true otherwise.
–
–
–
–
• A tautology is always true.
– P  Q  ¬ P  Q is a tautology.
– P  (Q  R)  (P  Q)  (P  R) is a tautology.
Semantic Networks
• Models meaning of language:
– Nodes correspond to word concepts
– Arcs are labeled with a property name or
relationship and link a node (word concept)
with another (value of property).
• Quillian (1967) introduced semantic
networks while others (Simmons -1973,
Brachman-1979, Schank-1979) have
extended the model.
Semantic Networks
Standardization of Relationships
• Standardization of relationships for representing
knowledge expressed in language
• focuses on case relations between verbs and
nouns in sentence (Fillmore ’68, Simmons ’73)
• Prepositions or articles indicate relationship
between verb and noun :
–
–
–
–
Agent : entity performing the action
Object : entity acted upon
Instrument : entity used in performing the action
Etc.
Conceptual Dependencies
Set of Primitive Actions
• Standardization of relations led to axiomatic approach to build
semantic model for representing meaning of language
Four Primitive Concept Classes
ACTS - Actions
PPs – Objects
(Picture producers)
AAs – Modifiers of
actions (Action Aiders)
PAs – Modifiers of
objects (picture aiders)
Each Action is assumed to reduce to one or more of the primitive ACTs
ATRANS – transfer relationship (give)
PTRANS – transfer physical location (go)
PROPEL
MOVE
GRASP
INGEST
EXPEL
MTRANS
MBUILD
CONC
SPEAK
ATTEND
Building Complex Conceptual
Dependencies
Conceptual
Dependency
PP  ACT
PP  PA
ACT  O PP
ACT  R PP

PP
Semantics
An actor acts
Object has attribute
Indicates object of action
Indicates the receipt
And donor of
An Action
Example
John  PTRANS … John ran
John  height
John is tall
John  Propel  O cart
John pushes the cart
John  ATRANS  R  John

 Mary
John took the book from Mary
Scripts
.
•
Scripts formalize stereotyped sequences of events
•
•
A script for a restaurant differs from one for a “fast food” model.
The components of a script are
– Entry conditions which must be true for script to be activated
– Termination conditions which are true when script is terminated.
– Props or object which support the script. The script for a restaurant would
include table and cash register props.
– Roles are the actions that individual participants must perform. The waiter takes
orders, the customer eats and pays bill.
– Scenes break the script into subsequences which
• Are sequential in occurerence
• Provide alternatives (if condition A then Scene1 elsce Scene2)
Frames
• Frames formalize stereotyped entities and actions.
• Frames have labeled slots with slot contents an object or action and
slot labels are the role played by the slot filler in relation to the
central entity of action.
• A frame is like a record that contains information relevant to
stereotyped action or entity:
– Frame Identification
– Relationship to other frames (part-of, caused-by)
– Slots
•
•
•
•
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Label indicating relationship to central slot
Requirements for slot filler
Procedural information to construct or manipulate slot contents
Default Contents
Slot contents
Frame Examples
Case Frame representation of
“Mary fixed the chair with glue”
Action
Fix
Agent
Mary
Object
Chair
Instrument
Glue
Time
past
Conceptual Graphs
A Network Language
• A conceptual graph is a refinement of
semantic networks.
• A conceptual graph is bipartite with one
class of nodes representing word concepts
and the other class of nodes representing
relations.
• Arcs go from concept class nodes to
relation class nodes and vise vesa.
Conceptual Graph Examples
Flies is unary relation or predicate
flies
bird
Color is a binary relation
dog
color
brown
Parents is a ternary relation
mother
child
mary
agent
parents
give
father
object
recipient
Mary gave john a book
book
john