Topics in Artificial Intelligence:
Intelligent Problem Solvers
This course is about building systems that can reason -that is, solve problems by utilizing Artificial Intelligence
techniques. For that, we shall assume that
Intelligence is a functional property independent
of any physical embodiment.
This is known as the physical-symbol system hypothesis
formulated by Newell and Simon in 1976.
There are other, less-symbolic AI paradigms, such as
neural networks and evolutionary computation.
What is Intelligence?
In most general terms, intelligence is a property attributed to people.
She is intelligent = She knows a lot.
= She thinks fast.
= She talks much.
= She learns quickly.
Intelligence = Knowledge + ability/capacity to perceive, feel,
comprehend, process, communicate, judge, learn.
What is Artificial Intelligence?
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An interdisciplinary field aiming at developing techniques and tools
for solving problems that people at good at.
Existing definitions of the field advocate everything from replicating
human intelligence to simply solving knowledge-intensive tasks. Some
examples:
“Artificial Intelligence is a study of complex information processing
problems that often have their roots in some aspect of biological
information processing. The goal of the subject is to identify solvable and
interesting information processing problems, and solve them.” -- David
Marr.
“Artificial Intelligence is the design, study and construction of computer
programs that behave intelligently.” -- Tom Dean.
“Artificial Intelligence is the enterprise of constructing a physical symbol
system that can reliably pass the Turing test.” -- Matt Ginsberg.
“Artificial Intelligence is the study of intelligence using the ideas and
methods of computation.” – Brady, Bobrow & Davis (in foreword to
“Building Problem Solvers” book).
Goals of Artificial Intelligence
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Scientific goal: understand the mechanisms behind human intelligence.
Engineering goal: develop concepts and tools for building intelligent
programs capable of solving real world problems. Examples of such
programs include:
– Knowledge-based systems. These capture human knowledge in a
particular domain, and are intended to solve problems from that domain.
– Common sense reasoning systems. These capture knowledge that
people commonly hold (which is why such knowledge is not explicitly
communicated), and are intended to do “everyday” reasoning.
– Learning systems. These posses the ability to expend their knowledge
based on the accumulated experience.
– Natural language understanding systems. These support dialog in
English/French/Japanese/… language.
– Game playing systems.
– Intelligent robots.
Artificial Intelligence Methodologies
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Classical problem solving: knowledge defines the so-called “problem space”, and a
general-purpose search (such as depth-first or breadth-first) is used as a problem
solving technique. Examples: the Boston subway problem (pp. 35) and the Algebra
problem solver (pp. 39).
Pattern-directed reasoning systems: knowledge is represented as “rules” (such as
“if A, then B”), and the so-called “search engine” identifies and fires rules which
antecedents hold. Example: the KM* system (pp. 92).
Truth Maintenance Systems: the latest AI methodology for efficient search and
generation of explanations for proposed solutions. This will be the main focus of our
course. We shall discuss different types of TMSs:
–
–
–
–
Justification-based TMSs.
Logic-based TMSs.
Assumption-based TMSs.
Contradiction-tolerant TMS.
We shall also discuss their example applications. As part of this discussion,
everybody will be assigned a research paper which must be carefully studied and
presented in class at a pre-announced time. This will count as homework 4.
Introduction to LISP
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Why LISP?
– Especially designed for symbol manipulation.
– Provides built-in support for lists.
– Automatic storage management (no need to keep track of memory
allocation).
– Interactive environment, which allows programs to be developed
step by step. If a change is to be introduced, only changed
functions need to be recompiled.
Recommended books:
Winston, Horn LISP, 3rd edition, AddisonWesley, 1993.
Norvig P. Artificial Intelligence Programming, Morgan Kaufman, 1992.
Basic terminology
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Atoms: word-like indivisible objects which can be numbers or
symbols.
Lists: sentence-like objects formed from atoms or other lists, and
enclosed in parentheses.
S-expressions: compositions of atoms and lists.
Procedures: step by step specifications how to do something.
– Primitives: procedures supplied by the LISP itself
Example: (+ 5 6)
– User-defined procedures: procedures introduced by the
programmer.
Example: (students 'anna)
Program: a collection of procedures working together.
S-expressions
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An s-expression can have other s-expressions nested in it. Examples:
(+
(* 5 7) ( / 2 4))
(This (is a dog) (or a cat))
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Expressions can be interpreted both, procedurally and declaratively.
– If interpreted procedurally, an expression provides a direction for
doing something. Such an expression is called a form, and its first
element is the name of a procedure to be used to produce the value.
– The process of computing the value of an expression is called
evaluation.
– If interpreted declaratively, expressions represent data.
Data and procedures have the same syntax.
Using Golden Common Lisp for evaluating sexpressions
GOLDEN COMMON LISP DEVELOPER 5.00
Copyright (c) 1984-1995 by Gold Hill, Inc., All Rights Reserved.
Versions:
COLDLOAD 5.002
GCLISP-FILE 2.1
LISPLIB 5.00
Top-Level!
* (+ (* 5 7) (/ 2 4))
71/2
* (This (is a dog) (or a cat))
Undefined function: THIS
*
Using Allegro Common Lisp for evaluating sexpressions
International Allegro CL Trial Edition
6.1 [Windows] (Oct 31, 2001 10:59)
Copyright (C) 1985-2001, Franz Inc., Berkeley, CA, USA. All Rights Reserved.
CG/IDE Version: 1.389.2.67.2.25
;; Optimization settings: safety 1, space 1, speed 1, debug 2.
;; For a complete description of all compiler switches given the current
;; optimization settings evaluate (EXPLAIN-COMPILER-SETTINGS).
[changing package from "COMMON-LISP-USER" to "COMMON-GRAPHICSUSER"]
CG-USER(1): (+ (* 5 7) (/ 2 4))
71/2
CG-USER(2): (This (is a dog) (or a cat))
Error: attempt to call `THIS' which is an undefined function.
[condition type: UNDEFINED-FUNCTION]
CG-USER(3):
Evaluation of atoms
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The value of a number is the number itself.
Example: 5 ==> 5
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The value of a string is the string itself.
Example: “Nice day” ==> “Nice day”
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The value of the symbol T is T (true).
The value of the symbol NIL is NIL (false).
The symbol NIL and the empty list ( ) are the same thing.
Variables are names of memory locations. The contents stored in a
given memory cell is the value of the variable serving as a name of this
location.
Example: Let x be a variable, and 5 be the contents of the memory cell called
x. Then, the value of x is 5.
Numbers
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Integers: 179, 45
Ratio: 5/7, 7/9
Floating point: 5.2, 7.9
Examples:
* (/ 25 5)
5
* (/ 46 9)
46/9
* (float (/ 46 9))
5.111111
* (round (/ 46 9))
5
1/9
; do not divide evenly
; the nearest integer
; the remainder
More numeric primitives
* (- 6)
-6
* (- -6)
6
* (max 5 7 2)
7
* (min 5 7 2)
2
* (sqrt (* (+ 1 3) (* 2 2)))
4.0
* (+ (round (/ 22 7)) (round (/ 7 3)))
5
* (+ 2 2.5)
4.5
* (expt 3 6)
729
* (sqrt 81)
9.0
* (sqrt 82)
9.055386
* (abs 6)
6
* (abs -6)
6
Representation of atoms and lists in a computer
memory
Consider the list (A (B (C))). It can be represented by
means of the following diagram:
A
These boxes are
called cons cells.
B
C
Each cons cell consists of 9 bytes:
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1 leading byte, called the data type byte. It holds
information indicating that the particular group of 9 bytes
is part of a list (i.e. a cons cell).
2 groups of 4 bytes each, representing pointers. Each
pointer is an address -- the first one to the memory location
containing the first element of the list, and the second one
to the memory location storing the rest of the list.
The second pointer of the last element of each list contains
zeros (representing NIL and empty list), i.e. no cons cell
corresponds to the empty list.
CONS builds new lists
Example: Given the list (Education is power), build a new list from it
and the atom University.
* (cons 'University '(Education is power))
(UNIVERSITY EDUCATION IS POWER)
To implement this, LISP maintains a list of free boxes (cons cells), called
the free-storage list. CONS removes the first box from the free-storage
list, and deposits new pointers into it.
Education
is
power
Free storage list
...
University
Dotted pairs
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Consider the list (A B . C). Here (B . C) is called a
dotted pair, and is represented as follows:
B
C
To construct the list (A B C), we write:
* (cons 'A (cons 'B (cons 'C NIL)))
To construct the list (A B . C), we write:
* (cons 'a (cons 'b 'c))