Artificial Intelligence
Fall 2008
Frank Hadlock
Definitions of AI
• The study of representation and search
through which intelligent activity can be
enacted on a mechanical device.
• The study of problems at which human
beings are currently more adept than
computers at solving and the translation
and improvement of human solutions into
forms which can be implemented on a
computer.
Physical symbol system hypothesis
The physical symbol system hypothesis (PSSH), first
formulated by Newell and Simon in their Turing Award
paper,1 states that “a physical symbol system [such as a
digital computer, for example] has the necessary and
sufficient means for intelligent action.” The hypothesis
implies that computers, when we provide them with the
appropriate symbol-processing programs, will be
capable of intelligent action. It also implies, as Newell
and Simon wrote, that “the symbolic behavior of man
arises because he has the characteristics of a physical
symbol system.”
History
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Graph theory & state space representation (Euler)
Boolean algebra – propositional calculus (Boole)
Predicate calculus – (Frege)
Descartes Discourse
Turing’s Test
Physical Symbol System Hypothesis
Connectionism
Discourse - Descartes
If there were machines which bore a resemblance to our bodies and imitated
our actions as closely as possible for all practical purposes, we should still have
two very certain means of recognizing that they were not real men. The first is
that they could never use words, or put together signs, as we do in order to
declare our thoughts to others. For we can certainly conceive of a machine so
constructed that it utters words, and even utters words that correspond to bodily
actions causing a change in its organs. … But it is not conceivable that such a
machine should produce different arrangements of words so as to give an
appropriately meaningful answer to whatever is said in its presence, as the
dullest of men can do. Secondly, even though some machines might do some
things as well as we do them, or perhaps even better, they would inevitably fail
in others, which would reveal that they are acting not from understanding, but
only from the disposition of their organs. For whereas reason is a universal
instrument, which can be used in all kinds of situations, these organs need
some particular action; hence it is for all practical purposes impossible for a
machine to have enough different organs to make it act in all the contingencies
of life in the way in which our reason makes us act. (Translation by Robert
Stoothoff)
Turing Test
The Turing test is a proposal for a test of a machine's ability to demonstrate
intelligence. Described by Alan Turing in the 1950 paper "Computing
Machinery and Intelligence," it proceeds as follows: a human judge engages in
a natural language conversation with one human and one machine, each of
which try to appear human; if the judge cannot reliably tell which is which, then
the machine is said to pass the test. In order to test the machine's intelligence
rather than its ability to render words into audio, the conversation is limited to a
text-only channel such as a computer keyboard and screen (Turing originally
suggested a teletype machine, one of the few text-only communication
systems available in 1950).
AI Application Areas
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Game Playing
Automated Reasoning
Expert Systems
Natural Language Understanding
Modeling Human Performance
Planning and Robotics
Languages for AI (Clips, Lisp and Prolog)
Machine Learning
Neural nets and Genetic Algorithms
Intelligent Agents
Game Playing and State Space Search
Board games can be represented by a usually large but
finite set of board configurations or states. The squares of
Tic Tac Toe can be numbered 1..9 and each configuration
as a sequence over {H,C,B} where many of the 39 cannot
occur because of order of play. A state BCBBBBBBB may
be followed by any of eight states obtained by replacing
any of the eight Bs by an H. BBBBBBBBB is the initial
state and any state with a row or column or diagonal
consisting of all Cs is a winning state for the Computer. If
the computer can find a path from start to winning state, the
path corresponds to a win for the computer and finding
such a path constitutes an example of artificial intelligence.
Graph theory: The city of
Königsberg
•The city is divided by a river. There are two
islands at the river. The first island is
connected by two bridges to both riverbanks
and is also connected by a bridge to the
other island. The second island two bridges
each connecting to one riverbank.
•Question: Is there a walk around the city
that crosses each bridge exactly once?
•Swiss mathematician Leonhard Euler
invented graph theory to solve this problem.
The city of Königsberg
Graph of the Königsberg bridge system
Euler Circuits
• A graph has an Euler circuit iff it is connected
and every vertex is of even degree.
• Necessity – Euler circuit enters a vertex each
time on a new edge and leaves the vertex on a
new edge. So vertex has degree 2 * number of
times on circuit
• Sufficiency – Pick starting vertex and traverse
graph, each time picking new edge. Can only
be blocked at start. Either have Euler circuit or
can pick vertex with unused edge on circuit and
build subtour starting with it. Splice subtour in.
Eventually will have used all edges once.
State space search
• Represented by a four-tuple
[N,A,S,GD], where:
•N is the problem space
• A is the set of arcs (or links) between
nodes. These correspond to the
operators.
• S is a nonempty subset of N. It
represents the start state(s) of the
problem.
State Space Search continued
• GD is a nonempty subset of N. It
represents the goal state(s) of the
problem. The states in GD are described
using either:
a measurable property of the states
a property of the path developed in the
search (a solution path is a path from
node S to a node in GD )
The 8-puzzle problem as state
space search
• states: possible board positions
• operators: one for sliding each square in
each of four directions,
or, better, one for moving the blank square in
each of four directions
• initial state: some given board position
• goal state: some given board position
•Note: the “solution” is not interesting here,
we need the path.
Eight Puzzle
1
4
7
5
8
3
1
4
3
6
7
6
2
2
5
8
State space of the 8-puzzle generated by “move blank”
operations
Traveling salesperson problem as
state space search
•The salesperson has n cities to visit and
must then return home. Find the shortest
path to travel.
• state space:
• operators:
• initial state:
• goal state:
Automated Reasoning and
Theorem Proving
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.
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• A tautology is always true.
– P  Q  ¬ P  Q is a tautology.
– P  (Q  R)  (P  Q)  (P  R) is a tautology.
Rules of Inference
• P , P  Q then Q - modus ponens
• ¬ Q, P  Q then ¬ P - modus tollens
Expert Systems
General problem solving has been attempted in AI but without success. Instead, systems
have been developed which specialize in domain-specific knowledge such as medicine.
People who work in these areas are called domain experts and solve problems by using
domain-specific rules which are applied to facts or knowledge in the knowledge base.
General problem classes solvable by expert systems (which replace the domain experts)
are diagnostic problems (backward chaining) and design or configuration problems
(forward chaining). When a path is found from a condition backward to a set of facts
causing the condition (or vise versa), the path corresponds to a diagnosis (or design) and
finding such a path constitutes an example of artificial intelligence
Natural Language Understanding & Semantics
Translation from text in one natural language to another requires more than vocabulary
substitution because of the inherent ambiguity of natural languages. To resolve this
ambiguity requires contextual knowledge in the form of a world model. As an example, a
punctuation symbol “,” can have the meaning of a list separator, or be used in place of
“then”, or be used to delimit a dangling modifier. Another example is the transaltion of
“hydraulic ram” in English into the Russian equivalent of “water goat”. In this last
example, a world model would say that there is such an animal as a “water buffalo” but
not a “water goat”. Translation usually involves syntactic analysis followed by semantic
analysis and a translation path from source to target constitutes an example of artificial
intelligence
Modeling Human Performance
Much of artificial intelligence is concerned with duplicating or surpassing human ingenuity on the
computer with no concern with how humans perform. Cognitive modeling is concerned with using
computers to determine human performance. Computer based tutoring is an example which has been
applied to tutoring algebra students to solve word problems. Cognitive modeling systems such as
ACT model human performance with rules or productions. The tutor interacts with the student by
posing a problem and then posing questions, attempting to guide the student to a correct solution.
By examining the responses, the tutor either poses another question corresponding to a correct step in
the solution, or diagnoses an incorrect “buggy” rule being used by the student. In this case, the tutor
reverts back to a previous concept needed in the correct solution. A path from problem statement to
any intermediate state constitutes an example of artificial intelligence
Planning and Robotics
Discussion of planning and robotics here is confined to motion planning in two dimensions. A basic
assumption in this discussion is that the Euclidean coordinates are available for the position of the
robot, of obstacles, and of goals. Motion planning is accomplished by working with the state space of
positions where positions are connected by an edge if there is no intervening obstacle. A path from
initial position to a goal position is a solution to the problem of motion planning that constitutes an
example of artificial intelligence.
Cognitive AlgebraTutors
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Algebra class may be less difficult and a bit more fun these days, thanks to research on how human cognition
works. Developed over two decades by psychologist John Anderson, the Adaptive Character of Thought (ACT-R)
theory is a framework for understanding how we think about and attack problems, including math equations. The
theory reflects our understanding o human cognition based on numerous facts derived from psychological
experiments.
ACT-R suggests that complex cognition arises from an interaction of procedural and declarative knowledge.
Declarative knowledge is a fairly direct encoding of facts (such as Washington, DC is the capital of the United
States, 5 + 3 =8); procedural knowledge is a fairly direct encoding of how we do things (such how to drive or how
to perform addition). According to the ACT-R theory, the power of human cognition depends on how people
combine these two types of knowledge.
Significance
The ACT-R theory provides insights into how students learn new skills and concepts, and, in doing so allows
teachers to see where students may need extra practice to master the new work.
Practical Application
Dr. Anderson and colleagues at Carnegie Mellon University have used this research to develop cognitive tutors,
computer-tutoring programs that incorporate the ACT-R theory in the teaching of algebra, geometry and integrated
math. The tutors are based on cognitive models that take the form of computer simulations that are capable of
solving the types of problems that students are asked to solve. The tutors incorporate the declarative and
procedural knowledge imbedded in the instruction and monitor students’ problem solving to determine what the
students know and don’t know. This allows instruction to be directed at what still needs to be mastered and helps
insure that students’ learning time is spent in a more efficient manner. Students work on a concept until it is fully
understood. Students who are having conceptual problems will be drilled on in that area, while those who have
mastered the concept move on to other areas.
The most widely used cognitive tutor program – now known as Carnegie Learning’s Cognitive Tutor - combines
software-based, individualized computer lessons with collaborative, real-world problem-solving activities. The
program now serves more than 150,000 students in most of the nation’s largest school districts. Field studies have
shown dramatic student achievement gains where the program is in use.
In 2003, the U.S. Department of Defense Schools awarded a contract that will use Cognitive Tutor mathematics
curricula in its 224 public schools in 21 districts located in 14 foreign countries, seven states, Guam and Puerto
Rico. These schools have approximately 8,800 teachers serving 106,000 students.
Cited Research
Anderson, J. R. (1983). The architecture of cognition. Cambridge: MA: Harvard University Press.
Anderson, J. R. (1993). Rules of the Mind. Hillsdale, NJ: Erlbaum.
Lisp
Lisp is the first language used in Artificial Intelligence and is structured so that a list is either data or a
function call. In the case of a function call, Lisp uses prefix notation which means that the first
list item is the name of the function and the remaining items are the arguments. Lisp indicates
variables by a question mark. To illustrate
–
–
(forall ?x
(implies (cs_student ?x) (must_take ?x data_structures) ) )
(cs_student bill)
Would yield
–
(must_take bill data_structures)
Prolog
Prolog is a logic programming language based on predicate logic. Prolog uses capital letters for
variables and lowercase letters for predicates and constants and reverses the order for implication.
Instead of writing P  Q, Prolog orders implication as Q :- P. A comma is used to separate arguments
and for conjunction with a period marking the end of a sentence. To illustrate,
– cs_student(bill).
– must_take(data_structures, X ) :- cs_student(X)
The first sentence asserts a fact that “bill” is a cs_student while the second sentence asserts that any
cs_student must take data structures. Prolog is launched by a goal such as
– :- must_take(data_structures,Y) which would return
– must_take(data_structures , bill)
CLIPS
Clips organizes knowledge by using named fact templates
consisting of named slots. An example is the PAY template
with slots for hours and pay rate. The deffacts statement
creates initial facts accolrding to selected templates. An
example is the payroll statement which assigns an initial fact
of 44 hours and of a rate of $8 / hour.
Fact List
(deftemplate pay (slot hours)(slot rate))
(deffacts payroll ( pay (hours 44)(rate 8))
(status incomplete)
)
CLIPS
Clips infers new knowledge by using named rule templates
consisting of an antecedent which must match facts in the
fact list and a consequent which adds or modifies facts.
Fact List
Rule List
(defrule calculate_basic
?p <- (pay (hours ?h)(rate ?r))
(test (<= ?h 40))
=>
(assert (basic_pay (* ?h ?r)))
(retract ?p)
)
CLIPS
Rule List
(deftemplate pay (slot hours)(slot rate))
(deffacts payroll ( pay (hours 44)(rate 8))
(status incomplete)
)
Rule List
(defrule calculate_basic
?p <- (pay (hours ?h)(rate ?r))
(test (<= ?h 40))
=>
(assert (basic_pay (* ?h ?r)))
(retract ?p)
)
(defrule calculate_overtime
(pay (hours ?h)(rate ?r))
(test (> ?h 40))
(status incomplete)
=>
(assert (overtime (* (- ?h 40) (* ?r 1.5))))
)
(defrule calculate_regular
(pay (hours ?h)(rate ?r))
(status incomplete)
(test (> ?h 40))
=>
(assert (regular (* 40 ?r) ))
)
(defrule calculate_adjustedgross
(regular ?r)
(overtime ?o)
(status incomplete)
=>
(assert (adjusted_gross (+ ?r ?o)))
(assert (status done))
)
Neural Nets
An artificial neuron consists of inputs xi , I = 1..n, which have a value of 0 or 1. Each input xi can
collect a value from the environment or from the output of another neuron and an associated weight wi.
A neuron is activated if the sum of the weighted inputs wixi exceeds a threshold function f. The neuron
outputs a 1 if activated and otherwise outputs a 0. Two sets of points in 2 dimensional space are
linearly separable if they can be separated by a straight line. In this case, the points can be classified
by a single neuron which outputs a 0 for points on one side of the line and a 1 for points on the other
side. This classification is an example of artificial intelligence. The point sets classified by a logical Or
gate and those classified by a logical And gate are linearly separable but not those classified by an
Exclusive Or.
Genetic Algorithms
Genetic algorithms are based on a biological metaphor of evolving solutions to a problem. The
solutions are strings over some alphabet and are referred to as genes. Given an initial population P0,
each member gene is evaluated by a fitness function specific to the problem For example, for the
knapsack function, the gene might be a list of object indices to be included and the fitness might be
the wasted space in the knapsack. Members are selected based on fitness and offspring are created
using crossover and mutation operators to form the next population. The process halts after so many
populations and the most fit member of the final population is selected as the solution to the problem
Representation and Search
• Representation of Problem Information
– Propositional & Predicate Logic
– Semantic networks
– State Space
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set of problem states along with
transitions between states
and a set of start states and goal states.
a path from start to goal is a solution
• Search
– Techniques for finding a solution
Eight Puzzle
• Representation – The squares of the eight
puzzle can be represented by integers 1 ..
8 and 9 represents empty square.
• A state of the puzzle is a permutation of
1..9 where 1st three represent top row, 2nd
three represent middle row, and 3rd three
represent bottom row.
Eight puzzle transitions
• An eight puzzle transition consists of moving a square
numbered 1..8 into the adjacent vacant square which can
only be done if it is adjacent to the numbered square.
• Representation of a board configuration is a permutation
of 1..9 where 9 represents vacant square. Example –
132496758 represents 1st row 132, 2nd row 4 blnk 6, 3rd row
748.
• Since the blank is in the middle position, 3 can be moved
down, or 4 to the right, or 6 to the left, or 5 moved up.
• These transitions make 132496758 have neighbors
192436758, 132946758, 132469758, and 132456798.
Knowledge Representation
• Essential to artificial intelligence are
methods of representing knowledge.
Besides propositional and predicate logic,
a number of other methods have been
developed, including:
– Semantic Networks
– Conceptual Dependencies
– Scripts
– Frames
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 :
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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
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Scripts formalize stereotyped sequences of events
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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