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KNOWLEDGE REPRESENTATION. Classical cognitive science and Artificial Intelligence relied on the idea of “knowledge representation”. The Representational-Computational theory of mind. Knowledge consists of mental representations (mental symbols).

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KNOWLEDGE REPRESENTATION

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KNOWLEDGE REPRESENTATION


  • Classical cognitive science and Artificial Intelligence relied on the idea of “knowledge representation”


The Representational-Computational theory of mind

  • Knowledge consists of mental representations (mental symbols).

  • Thinking consists of the manipulation of these symbols.

  • These computations have effects on behavior or on other representations.


THE COMPUTER ANALOGY

  • The mind is like a computer.

  • A computer consists of:

    1) Symbols or data structures:

    • A string of letters, like “abc”.

    • Numbers like 3.

    • Lists

    • Trees

    • Etc.

      2) Algorithms (step-by-step procedures to operate on those structures).

      For instance, a procedure may “reverse” the order of elements in a list.


Computers and mind

COMPUTERS MIND

Data structuresMental representations

Algorithms Computations

Running programsThinking


“The fundamental working hypothesis of AI is that intelligent behavior can be precisely described as symbol manipulation and can be modeled with the symbol processing capabilities of the computer.”

Robert S. Engelmore and Edward Feigenbaum


  • A cognitive theory describes the mental representations (symbols) and the procedures or computations on these representations.

  • What kinds of representations are there?


Different theories have different views about how the mind represents knowledge.

The “symbols” could include:

IMAGES

LOGICAL SYMBOLS

RULES

CONCEPTUAL SYMBOLS (frames, scripts).


IMAGES

  • Empiricists and other philosophers believed that mental representations are mainly visual images.


  • It is clear that we sometimes think in terms of images.

  • In the exercise below, for ex., we must manipulate (rotate) images.


  • Most philosophers, however, believe that images cannot express many important features of abstract human thinking.

  • For instance, logical relations like “if… then”.


LOGIC

  • Another option involves using formal logic to model human thinking.

  • There are several systems of logic.

  • One system is the propositional calculus, also known as sentential logic.

  • Formulas like “P” or “Q” represent propositions like “Peter is in school” and “Mary is in school”.

  • A proposition is a statement that refers to a fact.


  • An expression is any sequence of sentence letters, connectives or parentheses.

  • For example:

    P —> Q

    A)

    PQE —> (QQF <—> P)))) ((

  • 22 —> 5 is not an expression


Not all expressions are well-formed.

Many expressions in the previous page were not well-formed.

A well-formed formula (wff) is an expression that follows certain rules:


  • A sentence letter by itself is a wff

    Example: P


2. If we add the negation symbol ~ to any well-formed expression, the result is a also well-formed.

Example: ~P

Note: Since ~P is well-formed, it follows from rule 2 that ~~P is also well-formed.

Note: ~ goes together with only one expression.

~PQ is not well-formed.


3. Given two well-formed expressions, the result of connecting them by means of &, —>, <—>, or V is also a well-formed formula.

Example: P, Q, and ~Q are all well formed, so the following are also well-formed:

P & ~Q

P <—> Q

P —> Q

Note: &, —>, <—>, and V must always go together with two wwfs. Otherwise, the expression is not well-formed.

Sample expressions that are not well-formed:

P <—>

&Q


4. No other expression is well-formed.


  • Exercise: Which of these are well-formed? Why, or why not?

    A & B

    ~P —> Q

    ~ (A & B)

    A V —>

    ~A

    ~


  • A —> B can be translated as:

    • If A, then B

    • B, if A

    • A is a condition of B

    • A is necessary for B

    • A is sufficient for B

    • B, provided that A

    • Whenever A, B

    • B, on the condition that A


  • A & B

    • A and B

    • Both A and B

    • A, but B

    • A, although B

    • A, also B


  • A V B

    • A or B

    • Either A or B


  • A <—> B

    • A if and only if B

    • A is equivalent to B

    • A is a necessary and sufficient condition for B

    • A just in case B


  • How would you write “neither A nor B” in the propositional calculus?

  • The sentence can be written in two ways:

    ~(A V B)

    (~A & ~B)


Exercise--Translate the following into the propositional calculus:

Maggie is smiling but Zoe is not smiling

If Zoe does not smile, then Janice will not be happy

Maggie’s smiling is necessary to make Janice happy.

If Maggie smiles although Janice is not happy, then Zoe will smile.

Use the following translation scheme:

A: Maggie is smiling

B: Zoe is smiling

C: Janice is happy


  • Maggie is smiling but Zoe is not smiling

    A & ~B


  • If Zoe does not smile, then Janice will not be happy

    ~B —> ~C


  • Maggie’s smiling is necessary to make Janice happy

    A —> C


If Maggie smiles although Janice is not happy, then Zoe will smile.

(A & ~C) —> B


  • The truth (T) or falsehood (F) of propositions are called TRUTH VALUES.

  • The logical systems that we are studying today only have two possible truth values: T or F.

  • Note: there are several systems of logic that involve three or more values.


  • A Truth Table (TT) gives every possible combination of truth values between propositions.


  • A Truth Table gives the meaning (the grammar) of logical sentences.

  • If we want to known the meaning of ~A, we just make a Truth Table.

    A~A

    TF

    FT

    If A is true, then ~A is false.

    If A is false, then ~A is true.


ABA&B

TTT

TFF

FTF

FFF

A & B is only true if both A and B are true. Otherwise, it is false.


ABA V B

TTT

TFT

FTT

FFF

A V B is false if both A and B are false. Otherwise, it is true.


A B A —> B

TTT

TFF

FTT

FFT

A —> B is true, except when A is true and B is false.


ABA <—> B

TTT

TFF

FTF

FFT

A <—> B is only true if A and B are both true or both false.


  • Logic is concerned with truth.

  • Its concern is how the truth or falsehood of one proposition depends on the truth or falsehood of one or more propositions.

    • For instance, if A and B are both true, then A → B must also be true.


  • A complex proposition, such as A <—> B is a truth function of simple propositions A and B.

  • Its truth values depend on the truth values of its components.

    • These components are simple propositions.


  • We can consider a well-formed formula like A —> B as an expression, and then use the previous rules to construct a new truth table.


Example:

Construct a TT for the expression

(P —> Q) V (~Q & R)

First write down all the possible combinations for P, Q, and R.

Construct first the table for P —> Q, then for ~Q, then for ~Q & R.

Now you can do a TT for the whole formula!


  • Construct a TT for the expressions

  • P V (~P V Q)

  • ~ (P & Q) V P

  • R <—> ~P V (R & Q)


  • A TAUTOLOGY is a formula that is always true.

  • For instance, P —> (~P —> Q)

    To prove this, please construct a truth table, and you will see that for every value of P and Q the whole formula comes out true!


  • Is P V ~ P a tautology?

  • What about ((P—> Q) —> P) —> P)?


  • An INCONSISTENT FORMULA is always false.

    Example:

    P & ~P


  • A wff that is neither tautologous nor inconsistent is contingent.

  • Is this formula tautologous, inconsistent, or contingent?

    (P <—> Q) —> (P V ~R)


  • A proposition that is always true (a tautology) is so general that it says nothing in particular.

  • Tautologies contain no information about the world.

    • Only contingent propositions give information about the world.


  • To repeat:

    • All propositions that assert some particular information about the world are contingent.


  • The modern theory of truth tables for propositional logic was developed by…

    …the philosopher Ludwig Wittgenstein in his book Tractatus Logico-Philosophicus.


  • Logicians are mainly interested in reasoning.

  • Logical reasoning begins with some assumptions or premises.

  • The philosopher then applies certain rules of reasoning to reach conclusions.

  • We are now going to study several rules of valid reasoning.


Two important rules

The Modus Ponens

P → Q

P

Therefore Q

The Modus Tollens

P → Q

~ P

Therefore ~ Q


Other rules

  • From the conjunction (&) of two sentences, we can always conclude either sentence.

    Example:

    P & Q

    P

    Q


  • From any expression, we can conclude any sentence that has it as a disjunct.

    Example:

    Given the proposition P, we can conclude all of the following:

    P V Q

    (R –> T) V P

    R&F V P


Another example:

P –> Q

(P –> Q) V (~P & F)

(P –> Q) V T


  • If there is a disjunction (V), and one of its terms is denied, you can conclude the other term.

    Example:

    P V Q

    ~P

    Q


  • Given two assumptions, an arrow can be introduced as shown in the following examples.

    Example:

    R

    P

    P  R


Another example:

~P V Q

P

Q

P  Q


  • The arrows can be eliminated:

    Example:

    P  Q

    P

    Q

    An interpretation of this example:

    If it is raining, I will bring an umbrella.

    It is raining.

    I will bring an umbrella.


  • We can introduce double arrows in the manner of the following example:

    P  Q

    Q  P

    P ↔ Q

    Q ↔ P


  • We can also eliminate the double arrows:

    P ↔Q

    P  Q

    Q  P


  • If we assume a sentence and its denial, we can conclude the denial of any assumption that appears before the two sentences. (This is called the indirect method or reductio ad absurdum)

    Example:

    P  Q

    ~Q

    P

    Q

    ~P


  • Exercise--Prove the following:

    P V ~R

    ~R  S

    ~P

    S


  • The rules we have studied are “truth-preserving”.

    • If we start from true assumptions and then apply these rules, the conclusions thus reached will also be true.

    • The rules preserve truth from the premises to the conclusions.

    • Truth is not lost if the rules are followed.


  • To reason is to construct proofs.

  • A proof is a sequence of lines.

    • Each line contains one sentence.

    • Each sentence is either an assumption or the result of applying the rules of reasoning to some assumptions.

    • The last sentence is the conclusion or theorem that is proved.


There are many very simple and important examples of logical reasoning that cannot be expressed in the propositional calculus:

All human beings are animals;

Bryan is a human being,

therefore Bryan is an animal.

Another example:

All positive integers are divisible by themselves.

2 is an integer,

therefore 2 is divisible by itself.


What is the problem?

Every sentence in this type of argument is different from every other sentence.

Different sentences are represented by different sentence letters (for instance, A, B, and C).

We cannot represent the similarities between the various sentences, because we take the whole sentence as a unit.

Propositional logic cannot show how it is possible to conclude the last sentence from the first.


  • We need to break down each sentence into parts, and then…

    …show how different sentences share the same parts.


We need another language

How to express the similarity between:

  • Sam is smiling

  • Janice is smiling ?

    We can represent them as follows:

  • Fa

  • Fb


  • Now, letters like a and b represent names, whereas F represents the predicate “is smiling”.

  • A proposition can be understood as relation between a subject and a predicate.


The sentence “Hector is Spanish” can be written as

Fa

where a = Hector and F = is Spanish.

The letter “a” represents “Hector”.

The letter is a name for the subject.

F represents the predicate.


  • It is clear that the following two sentences, although different, have the same structure:

    Hector is Spanish

    Picasso is Spanish

    One sentence can be represented as Fa (Hector is Spanish) and the other as Fb (Picasso is Spanish).


  • Many people are Spanish, not just Hector and Picasso.

  • We can make the expression more general by replacing the name “a” with a variable “x”.

    Fx


  • A propositional function is formed by replacing a name with a variable.

  • A function is more general than a proposition.

  • We use the word “function” to indicate that the language of logic is (or is very close to) the language of mathematics.


  • A function always has an empty place.

    For instance:

    “are animals”, “is Spanish”, and “is smiling” are incomplete expressions.

    • The subject is missing.

    • Only when it is complete can the sentence say something that is either true or false.


Problem:

  • if we take “x” to represent the general term “people”, then Fx represents “people are Spanish”.

  • But not all people are Spanish!

  • So we need to find a way to express that some people are Spanish.


  • In other cases, however, it is appropriate to say “all”.

    For instance:

    All people are rational animals.

    All people will die some day.


  • xFx indicates that the predicate F describes “all x”.

  • xFx indicates that the predicate F describes “some x”.

  • To indicate “all” or “some” is to quantify an expression.


  • This new logical language is focused on “propositional functions” like “x is Spanish” or “x is smiling”.

  • These functions are always quantified.


  • The logical system we are discussing is called the Predicate calculus.


THE PREDICATE CALCULUS

Elements

  • Names:

    a, b, c, d, a1, b1 , c1,, d1 , a2, …

    Names represent individuals, like “Tim” or “this chair”

    2. Variables

    u, v, w, x, y, z, u1, v1 , w1 , …


3. Predicate letters:

A, B, C,… Z, A1, …. Z1, A2, …

4. The identity symbol ‘=‘


5. Quantifiers:

a) The universal quantifier x

The universal quantifier corresponds to “every” or “all”.

b) The existential quantifier x

The existential quantifier corresponds to “some”, which means “at least one”.

A quantifier must always be followed by a variable (never a name).


6. All the elements of the propositional calculus: sentence letters, connectives, and parentheses.

Note:

The Predicate Calculus is an extension of the propositional calculus.

It includes the same elements plus several new ones (names, variables, predicate letters, and the identity symbol).


For convenience, we can also introduce the symbol  as an abbreviation.

a  b really means ~a = b.

The symbol  is not really part of the basic vocabulary of the Predicate Calculus.


Rules of well-formed formulas in the Predicate Calculus

1. All the rules of the propositional calculus also apply to the Predicate Calculus.


2. A predicate letter followed by one or more names is well-formed

Examples:

  • Fa

  • Fab


3. Expressions of the form a = b (identity of names) are wff.

Strictly speaking, identity is a kind of predicate.

The proper way of writing this should be

=ab

For historical reasons, however, it is written a=b.


  • 4. Any name in a wff can be replaced by a variable, the result is also well-formed if it is quantified.

  • For instance, if Fa is well-formed, then we can:

    • Replace “a” by “x” and form Fx.

    • Quantify the new sentence as xFx.


  • When we use variables, we must quantify:

    Fx is not well-formed.

    • It is an example of an open formula.

    • (An open formula is made by replacing a name in a wwf with a new variable without quantifying the variable).


  • Fx and Fx are not well-formed.

    • x Fx and x Fx, however, are well-formed.

  • aFa and bFb are not well-formed.

    • You cannot quantify a name, only a variable.


5. Nothing else is well-formed.


Are the following wff?

  • Fz

  • Fb

  • xGab

  • xGax

  • x (Gxy <—> yHy)

    (Hint: There is only one wff here!)


Translate the following sentences:

  • All Spanish men are clever

  • Some Chinese people live in Hong Kong

  • Not all Chinese people live in Hong Kong

  • Only Spanish people live in Madrid

  • No people study in City University unless they are stupid.


  • All Spanish men are clever

    x(Sx —> Cx)


2. Some Chinese people live in Hong Kong

x(Cx & Hx)


3. Not all Chinese people live in Hong Kong

~x(Cx—>Hx)

Alternative form: x(Cx & ~Hx)


4. Only Spanish people live in Madrid

(M = Live in Madrid; S = is Spanish)

x(Mx—>Sx)

The formula x(Sx—>Mx) is an incorrect translation!

Why is it incorrect?


5. No people study in City University unless they are stupid.

(P = are people; U =study in CityU; S = are stupid)

x(Px —> (~Ux V Sx))

Another form: x((Px & UX) —> Sx)


How to indicate that there are exactly n things?

For instance, exactly one, or exactly two, etc.

xy x=y Exactly one

xy (xy & z (z=x V z=y) Exactly two

xyz (((xy & xz) & yz

& w ((w=x V w=y) V (w=z)) Exactly three


  • Quantities are always expressed by using:

    The identity symbol = ,

    together with

    Quantifiers.


  • In addition to the rules of propositional logic, several new rules are helpful.

  • To explain them, we need to explain three concepts:

    • Universalization

    • Existentialization

    • Instantiation


  • We have already introduced the important procedure of universalization.

    For instance:

    Take the formula Fa & Ga.

    • x (Fx & Gx) is a universalization of that formula.


  • Another procedure is existentialization.

    For instance:

    Take the formula Fa & Ga.

    • x (Fx & Gx) is an existentialization of that formula.


The reverse of existentialization and universalization is instantiation.

The formula Fa & Ga is an instance of the formula x (Fx & Gx) and of the formula x (Fx & Gx).


  • We can now formulate several rules of reasoning.


  • For any universally quantified sentence, we can conclude any instance of that sentence.

    Example:

    x Fx

    Fa

    Fb


  • Given a sentence with one name, we can conclude an existentialization of that sentence:

    Example:

    Fa

    xFx


  • The following argument is not valid:

    Fa

    x Fx

  • You cannot conclude that, just because something is F, therefore everything is F!


Here is a simple chain of reasoning:

x(Fx—>Gx)

Fa –> Ga

Fa

Ga

Fa &Ga

x (Fx & Gx)


Exercise:

Prove:

x (Gx & ~ Fx)

x(Gx –> Hx)

x (Hx & ~ Fx)


x (Gx & ~ Fx)

x(Gx –> Hx)

Ga –> Ha

Ga & ~Fa

Ga

Ha

~Fa

Ha & ~Fa

x (Hx & ~ Fx)


Quantifier exchange

Example:

x ~Fx can be turned into:

~x Fx

Example:

~ x Fx can be turned into:

x ~Fx


Leibniz’s Law (Substitutivity of Identity)

  • If a=b, then a and b can be interchanged in any sentence.

    Example:

    Fa

    a=b

    Fb


Another example of Leibniz’s Law:

Fa & Ga

a=b

Fb & Ga

Fb & Gb

Fa & Gb


  • That identical terms can be substituted for one another is an extremely important law of logic.

  • Some philosophers, such as Frege, believe that it is one of the most important.


  • We can use this law to prove that if a=b and bc, then ac.


  • Please remember that we have simplified the laws of reasoning.

    Take this as an introductory overview…


  • Formal logic can be used to construct plans.

  • A plan is a logical deduction from some initial state to a goal state.

  • Planning has been very important in the theory of Artificial Intelligence.


CRITICAL QUESTIONS ABOUT LOGIC AND COGNITION

  • Formal logic was developed to provide an ideal standard of excellent thinking.

  • It was not developed to describe how human beings actually think in their everyday lives.

  • Many scholars believe that ordinary people do not typically use formal logic in their plans.

  • Logic has nothing to do with psychology or actual cognition.


  • Psychologist Peter Wason developed a method of testing whether people do tend to apply logical rules in their everyday thinking.


The four cards above appear on the page.

A rule states:

If one side has a word, then the other has an even number

(In short: if word, then even)

  • Your task is to decide which cards must be turned to see if the rule is true of the four cards.

  • Turn only the minimum number.

  • Most people turn the two cards with words on them to check the other side.

  • This can be seen as an application of the modus ponens rule.


  • Many people fail to turn over the 7.

  • They often say they have not done so because:

    The rule doesn't say anything about odd numbers.

    But if the 7 card has a word on the other side, then the rule would be refuted.

    So it is necessary to turn over the 7.

    To understand this, people need to know the modus tollens.


  • The point of the experiment is that logical rules do not quite describe how people actually reason.

    • People normally use representations and procedures very different from those of formal logic.


The problem of consistency.

Most logicians insist that systems should be consistent.

This requirement is too strong.

Human thinking is often inconsistent.


  • Classical logical laws are supposed to apply with unrestricted generality.

  • Many people, however, treat rules as rough generalizations that admit of exceptions.

    • A rule is often treated as a default.

  • The rule that if x is an SCM student, then x is stupid is roughly true, but there are exceptions.


  • Traditional logical thinking is mainly sequential.

  • It does not account for other forms of thinking, such as lateral thinking.

  • "Lateral Thinking aims to change concepts and perceptions“.

  • Lateral thinking involves searching for different ways of looking at things.

  • It involves looking at a situation from a new angle or POV.

  • “With logic you start out with certain ingredients just as in playing chess you start out with given pieces. In most real life situations, we assume certain perceptions and certain concepts. Lateral thinking is concerned not with playing with the existing pieces but with changing those very pieces”


  • A lateral thinking puzzle:

    A father and his son are involved in a car accident, as a result of which the son (but not the father) is rushed to hospital for emergency surgery.

    The surgeon looks at him and says "I can't operate on him, he's my son".


  • Computer scientist Marvin Minsky insisted that the influence of logic (particularly the issue of consistency) has been harmful to AI research.


  • The weaknesses of any logical approach to AI can be considered in relation to the Frame Problem


Suppose that we define a world.

A state of this world will include:

  • Objects (e.g., cubes A, B, and C)

  • Relations between objects (e.g., location)

  • Properties of objects (color, shape, etc.)


  • An event in this world is a relation on states (a function that maps one state to another state).

  • Examples:

    • Put one object on another.

    • Move one object from one location to another.


  • Suppose block B stands on block A.

  • One robot must move block A to a new location.

  • We have only moved block A. But of course, this implies implies that block B has also been moved.


  • In a complex world, one single change will produce many other changes.

  • Knowledge of the world is interdependent.


  • In normal cases, people do not consider everything that does not change.

    • For instance, when an object is moved, its color and shape will normally not change. If it is blue, it will remain blue; etc.

    • These are irrelevant factors.

  • It is obviously out of the question to write a long list of logical rules specifying all that does not change.


  • In most everyday situations, there is a potentially unlimited number of relevant features.

  • How can we avoid specifying everything that does not change?

    This is known as theframe problem.

  • The frame problem arises in the context of reasoning about the effects of certain actions on the world.


The frame problem arises especially when a goal requires a sequence of events or actions.

The following problems can occur:

  • To miss one of the possible consequences of some event.

  • To waste resources examining facts that are completely irrelevant.


  • Many cognitive scientists believe that all assumptions involved in thinking can be represented EXPLICITLY by means of symbols (for instance, mathematical or logical symbols)

  • But the frame problem shows that many assumptions involved in thinking cannot be explicitly represented.

    • They must remain implicit. 


  • This problem is not just about robots.

  • The frame problem raises important philosophical questions about the nature of mind.


  • Disappointed with the logic-based approach, AI researchers like Marvin Minsky have looked for alternative ways to represent knowledge.

  • Some alternatives include:

    • Frames

    • Scripts

    • Rules


FRAMES

  • When we come across some situation, we select from memory a structure, called a frame.

  • A frame is "a data-structure for representing a stereotyped situation” or category.

  • A frame is a mental representations of typical things and situations related to some concept.


  • For instance, the FLYING ON A PLANE frame includes the following categories:

  • FLIGHT ATTENDANT, LIFE VEST, SAFETY BELT, FIRST CLASS, ECONOMY CLASS, SAFETY INSTRUCTIONS, etc.

  • There are relations between these categories (X has a Y, X is on Y, X is a part of Y, X is a kind of Y, etc.)

  • Both the categories and their relations are part of the frame.


  • The frame FLYING ON A PLANE must also include “subframes” like:

    • GOING TO THE TOILET,

    • WATCHING A MOVIE,

    • FINDING ONE’S SEAT,

    • STORING ONE’S HAND LUGGAGE OVERHEAD, etc.


  • A frame models our expectations and assumptions.

    • If we see certain kinds of doors, we expect to find a room behind it.

    • And we have some assumptions about what a normal room must look like (it may have windows and shelves, etc.)


  • One important difference between the frame-based approach and the logic-based approach:

    • The frame approach was designed mainly to study psychology and AI.

    • Logic was not designed for psychological research.


Example: The concept of a “Western”.

A kind of fiction

Normally takes place in the US

Set around or after the US Civil War

Characters: sheriff, cavalry officer, farmer, cattle driver, bounty hunter.

Locations: small town, fort, saloon, stagecoach

Objects: guns, horses, roulettes, etc.

Typical situations: gunfights, burning a farm or a fort, stampede, driving cattle, etc.

Film Examples: Unforgiven, Rio Bravo, Fort Apache, My Darling Clementine.


  • A frame is a package of information that can be applied as a whole.

  • According to this sort of theory:

    Cognition does not consist of step-by-step logical deductions.

    It is the application of a whole frame to a particular situation.


Information is often structured into “parts” and “wholes”.

The act of looking at a cube, for instance, involves a structure like this:


  • A frame can be represented as a graph of nodes and relations.

  • The top levels tend to be more “fixed” and stable.

  • The lower levels consist of “terminals” or slots that can be filled by data.


When we move around a cube, one or more faces may go out of view, the whole shape of the cube may change, etc.

Thus we have a series of view-frames.


  • Some relations are more stable than others.

  • For instance, “next to” is more stable than “top” and “bottom”.


  • Do we build such frames for every single object?

    • This sounds too complicated.

    • People probably just build frames for important objects and for a few simple or basic shapes (cube, sphere, cone, etc.)


Default assignments

Minsky hypothesized that frames are stored in long-term memory with default terminal values.

For instance, if I say “Peter is on the chair” you probably do not think of an abstract chair. You perhaps imagine a particular chair with a shape, color, etc.

These characteristics are default assignments to the terminals of frame systems.


  • If needed, default assignments can be changed to fit reality.

    • A frame can adapt, if the data do not match our expectations or assumptions.

    • Surrealist artists force us to modify many of our default expectations.

    • We open a door and there is not a room but a landscape!


  • What happens when the data do not match the frame?

    1. We can replace our original frame choice with another frame.


2. We can find an excuse or an explanation.

“It is an experimental movie”.

“It is broken or poorly designed”.

“It is not finished”.

“It is not a real door but a toy”.


3. When trying to replace a frame, we can use advice from a similarity network.


This network represents similarities and differences between related concepts.

A box, unlike a table, has no room for knees; the box is similar to a chair because one can sit on it, etc.

If something is not a chair, perhaps it is a box!


In this way, similarity networks can help us to replace our original frame with a more appropriate frame.

Frames are thus open to change.


Frame modification or replacement resembles the scientific process:

  • Producing a hypothesis (a frame)

  • Testing it (matching the frame against the data)

  • Modifying or replacing it.


  • A key idea behind the theory of frames:

    The basic ingredients of intelligence are typically structured into chunks of some sort.

    These structures are open to revision.

    The use of changeable structures accounts for the power and efficiency of human thinking.


  • In film, we can think of the following as examples of frames:

    • Popular genres (martial arts, action, sci-fi, ghost, Western, detective, romance).

    • Narrative (story) structures: the classical Hollywood structure.

    • Documentary or Fiction

    • Individual “authors”: such as the style of a famous director.

      Films can encourage us:

  • To search for the right frame, when it is not clear which frame is relevant

  • To revise the frame in the course of a film by maintaining an inconsistent or changing frame.


  • Some scholars prefer the word “schemata”.

    A schema is roughly the same as a frame:

    “A schema is a knowledge structure characteristic of a concept or category. “ (David Bordwell)

  • Schemata are embodied in prototypes, or "best examples."

    • Our prototype of buying and selling probably involves one person purchasing something from another with cash, check, or credit card.

  • This prototype is a sort of default assignment.

  • On the basis of the schema, people can apply the same essential structure to a variety of differing situations.


  • This approach has often been applied to the study of art.

  • Viewers (readers, etc.) must actively search for frames or schemata that match the data of the art work.

  • The art work can thus engage the active participation of viewers.

  • When an artist is aware of cognition, s/he will invite users to participate by using ambiguous or changing frames.

  • Artists can also presuppose unusual frames.

  • Our experience will become dynamic and rich.


SCRIPTS

  • In addition to frames, an alternative way to model conceptual thinking involves scripts.


  • A SCRIPT is a knowledge structure specifically designed for typical event sequences.


  • A famous example is the [RESTAURANT] script developed by the computer scientist Roger Schank and the social psychologist Robert Abelson in 1977.


  • THE RESTAURANT SCRIPT       1) Actor goes to a restaurant.       2) Actor is seated.       3) Actor orders a meal from waiter.       4) Waiter brings the meal to actor.       5) Actor eats the meal.       6) Actor gives money to the restaurant.       7) Actor leaves the restaurant.

  • The underlined words represent variables.


  • A script can be understood as a sequence of conceptualizations, with some variables in them (called script variables).


  • The script often involves branching:

    • If you arrive in a restaurant, it may be that either there is a menu already on the table or that the waiter will bring you one.

    • Eventually, you will go on to order your meal, so the two branches will join again.


  • A script enables you to “fill in” unstated or missing information.

    • Think of a movie where you see a character walking out of a house and (in the next scene) into a restaurant.

    • You infer that the person walked or took some form of transport between the two scenes.

    • Later, you can assume that the person paid for the dinner, even if this is not shown in the movie.


  • A script may also include:

    • “props” (table, menu, food, silverware, plates, money, bill)

    • roles (waiter, customer)

    • perhaps some entry conditions (the customer is hungry, the customer has money, the customer likes the restaurant)


  • Like frames, scripts are also open to revision.

  • Parts of a script can be adapted to changing circumstances.

  • New parts can be added to existing scripts.


RULES

  • Another model of reasoning involves the use of “rules”.

  • A rule is an IF-THEN structure.

    • The “if” part is called the condition.

    • The “then” part is called the action.


  • A rule may be taken as a default.

  • A default is a rough generalization that may be changed when exceptions appear.

  • In this sense, rules are not fixed once and for all.

    • For instance: IF x is a bird, THEN x can fly.

    • A penguin is an exception…

  • These “rules” are different from classical logical rules, which do not admit of exceptions.


Rules can represent many sorts of knowledge about (for example):

Concepts and their relations.

“If x has four legs, wags its tail, and barks, then x is a dog.”

IF x is a dog, THEN x is a mammal.

Causes and effects in the world

If x is kicked, then x will move.

Goals or tasks

IF you want to obtain a better job, THEN you should get a degree from a good university.

Regulations

IF you do not attend the exam, THEN you will fail the subject.


  • Rules can be arranged hierarchically in tree form:

    • There are rules having other rules under them

    • For instance, the rule for recognizing dogs includes a rule for recognizing tails.


  • The concept of “rule” was not developed as an ideal logical tool.

    • It was different from the predicate and propositional calculus.

  • The rule concept was developed to model real human thinking.

  • In particular, rule systems are used to model problem-solving.


  • Allen Newell, Cliff Shaw, and Herbert Simon (NSS) developed the field of Artificial Intelligence in 1955.

  • They understood intelligence as the capacity to solve problems.

  • A problem consist a gap between some starting state and some goal state.

    • Examples: find a way to exit the house and start the car, find something to say in response to a certain statement, choosing the right school, finding the fastest path to reach a destination, etc.


  • To solve a problem means…

    ….to find a sequence of rules that gives a path from the starting state to the goal state.

    These rules are a plan or strategy for action.

    Work in classical AI often described intelligence in terms of planning.


  • Rules can be used to think forward or backward.

    • We can either work forward from the starting point or backward from the goal.

  • Example of backward thinking:

    • If I want to reach school, I might reason thus: “To get to school, I must take the highway. To reach the highway, I must take the main street. To reach the main street…”

    • In forward thinking, however, I would start out from the house and consider all possible choices.

  • Another strategy is bidirectional search.

    • This approach combines backward and forward thinking.


  • When you have to solve a problem, you must often SEARCH through a space of possibilities.

  • For instance:

    • If you are trying to find your way out of a maze, you must search through the space of possible paths.

    • If you are looking for a good design for a car, you must search through the space of possible designs.

    • You might want to search through all possible combinations of colors in order to pick the right combination of clothing.


  • In a logical system, the main operation is “deduction” (proving formulas from the axioms plus the rules of proof).

  • In a frame-based theory, the main operation is the application of a frame to a given situation.

  • In a rule-based system, however, the main operation is SEARCHING THROUGH A SPACE OF POSSIBILITIES.


  • In many cases, however, the space of possible solutions is too large.

    • It is not practically possible to search through the entire space.

  • To try every possible solution would be highly inefficient.


  • Consider how actual people conduct efficient searches.

    • For instance, a doctor diagnosing an illness does not need to go through every possible cause.

    • Her knowledge leads her to narrow down the search space considerably.

    • We say that she is an expert in this area.

  • Knowledge relevant to a problem can reduce search time. This is the essence of expertise.


  • For instance, if I already know a city, I can use my knowledge of landmarks, streets, and neighborhoods to find a particular location.

  • Knowledge-search duality:

  • “Search compensates for the lack of knowledge”

  • “Knowledge reduces uncertainty by reducing search.”


  • Expertise combines two kinds of knowledge:

  • Knowledge of facts

  • Practical heuristics acquired through years of experience and trial and error.

    • These include the tricks, shortcuts, and rules-of-thumb that experts have learnt through years of experience.

    • Heuristics are rules that can help you find a good enough solution without having to search through the complete space of possibilities.


  • An Expert System contains large amounts of very specific, specialized knowledge (ie., knowledge of a narrow area) about complex problems.

  • “Expert systems” (ES) and “Knowledge-based systems” (KBS) are often used synonymously.

  • Building an expert system is known as knowledge engineering.


  • Knowledge engineering begins by interviewing experts in various fields (science, medicine, business) to find out how they think.

  • Expertise is then reduced to a set of interconnected general rules, the knowledge base (normally if-then rules, but possibly also frames).


Sample rules

  • IF engine_getting_petrolAND engine_turns_overTHEN problem_with_spark_plugs

  • IF NOT engine_turns_overAND NOT lights_come_onTHEN problem_with_battery

  • IF NOT engine_turns_overAND lights_come_onTHEN problem_with_starter

  • IF petrol_in_fuel_tankTHEN engine_getting_petrol


  • A reasoning or inference engine then matches new evidence against this knowledge base.


A complete interaction with the car repair system might be:

System: Is it true that there's petrol in the fuel tank?

User: Yes.

System: Is it true that the engine turns over?

User: No.

System Is it true that the lights come on?

User: No.

System: I conclude that there is a problem with battery.


  • http://www.expertise2go.com/webesie/tutorials/ESIntro/

  • http://easydiagnosis.com/


  • Expert systems can be used in game design.

  • Baseball simulation games, for instance, were often based on expert knowledge from baseball managers.

  • When a human played the game against the computer, the computer asked the Expert System for a decision on what strategy to follow.

  • Even those choices where some randomness was part of the natural system (such as when to throw a surprise pitch-out to try to trick a runner trying to steal a base) were decided based on probabilities supplied by expert sportsmen.

  • Tony La Russa Baseball

  • http://www.mobygames.com/game/dos/tony-la-russa-baseball-ii/cover-art/gameCoverId,32721/

  • Earl Weaver Baseball

  • http://www.sportplanet.com/features/articles/ewb/


  • The medical expert system Mycin represented its knowledge as a set of IF-THEN rules with certainty factors.

  • It was coded in Lisp.

    The following is an English version of one of Mycin's rules:

  • IF the infection is pimary-bacteremia AND the site of the culture is one of the sterile sites AND the suspected portal of entry is the gastrointestinal tract THEN there is suggestive evidence (0.7) that infection is bacteroid.


  • The use of expert systems in some professions, such as medicine, can give rise to legal issues.

  • The system Mycin, developed for medical diagnosis in the 1970s, was never actually used in practice.

  • This wasn't because of any weakness in its performance - in tests it outperformed members of the Stanford medical school.

  • It had to do with legal issues:

    • If it gives the wrong diagnosis, who do you sue?


  • The following art work can be understood as a parody of questionnaires.

  • http://www.diacenter.org/closky/


PROBLEMS WITH EXPERT SYSTEMS


The core problem

Cognitive science and AI researchers often believe that:

  • people carry a list of background assumptions inside their minds

    (This list may involve rules, frames, and/or scripts)

  • This list of background assumptions could be completed in theory, so that all assumptions could be enumerated completely, and then coded in some form in a computer.

    Do these two beliefs make sense?


  • Most human experts do not know explicitly all the things that they know implicitly or non-consciously.

    • It is like tying up our shoes, something that we do without thinking of the complicated steps involved.

    • The knowledge is not the object of conscious attention.

  • People who have strong expert knowledge may not be able to explain what that knowledge involves.


  • If we only ask them, we may never obtain any information on “intuitive” or “non-conscious” knowledge.

  • Experts often use common sense and intuitive knowledge, which are not easily programmable.


  • There is a difference between knowing-how and knowing-that.

    • Knowing-how (procedural knowledge) involves task-oriented skills.

    • Knowing-that is the knowledge that a statement is true or false.

  • A lot of our knowledge is “knowing-how”.

  • Is it possible to put all of this procedural kowledge into words?


  • The problem: how to encompass all of intuitive knowledge in a finite system of rules?


  • In practical terms, classical AI had serious limitations.

  • The classical AI approach can give incorrect responses for questions that lie just slightly outside of the narrow areas for which they were programmed.

  • These practical problems suggest a strong problem with the philosophical suggestions.


  • Most of our actions are social (they involve or presuppose more than one person).

  • Social action relies on background knowledge:

  • Background knowledge is taken for granted by all participants in an interaction.

  • It is shared by all participants.

  • Seldom put explicitly into words.


  • Any system of rules in the real world is incomplete.

  • Knowledge may not involve any data structure at all:

    • For instance, I can learn to ride a bicycle simply by practicing certain patterns of body responses acquired through trial and error, imitation, practice, formal or informal training, etc.

  • How do you know the difference between the sound of a violin and the sound of a cello? Is it a matter of learning a system of rules?


Some critics complain that classical AI overemphasizes rules and planning.

What is planning?

  • A plan controls the order in which a sequence of actions is to be carried out.

  • From this point of view, the execution or implementation itself is unimportant: every move is a stage in the implementation of the plan.

  • Action is controlled by a plan.

  • Is this an accurate model of human thinking?


  • The world is too dynamic and unpredictable and for this reason cannot be completely and reliably represented inside the machine.

    • Our plans are essentially vague.

    • Plans do not represent the circumstances of actual actions in full detail: they could not possibly do so!

      “No amount of anticipation, planning, and programming can ever enumerate, a priori, all the variants of even a routine situation that may occur in daily life.”

      George N. Reeke and Gerald Edelman

      “In the real world any system of rules has to be incomplete.”

      Dreyfus


  • If we take “plans” to determine every aspect of action, then our actions are never planned in this strong sense.

  • A plan does not specify everything that a person must do next.

  • Even a detailed plan requires some improvisation on the spot.

    • Improvisation is by definition not bounded by plans.

    • People respond to their situations: the material and social circumstances of their actions.

    • At most, a plan is only a rough guide.


    • This does not mean that people never plan or use rules.

    • People do make plans and use rules, quite often..

      …but plans do not control every aspect of an action.

      • Let us consider this point in detail:

    • How do we use planning?

    • Plans are “imagined projections” that we use to prepare for an action before it happens.

    • They are also “retrospective reconstructions” that we use to explain an action that has happened or to review its outcomes.

    • Plans come before or after action.

    • Plans are resources for our practical thinking about action.


    • Sometimes we use plans while conducting an action…

      …But only because the action has somehow run into problems.

    • This is not the “usual” or “normal” situation.


    • The system of our assumptions is essentially vague:

    • There is no finite list of rules or assumptions that could be completely coded into a computer.


    • The problem is that classical AI and cognitive science emphasize knowledge representation.

    • They assume that knowledge of the world is represented inside the mind, in the form of symbols that code rules, frames, scripts, etc.

    • Cognition does not only happen “in the head”.

    • It is a complicated, interactive achievement that involves:

      • The body and skills of the person.

      • Interaction with the environment (including other persons).


    • Classical AI studied individual minds.

    • It ignored the extent to which intelligence involves the environment, including other people or agents.


    • For instance, the meanings of words or sentences depend on the context in which they are used.

    • Language is essentially 'indexical'.

      • It can only be understood in relation to its surrounding context.


    Situated action

    • Lucy Suchman used the term “situated action” to emphasize “that every course of action depends in essential ways upon its material and social circumstances.”


    • People’s behavior is often regular.

    • It is not random.

    • But this does not mean that people carry a list of complete and precise rules in their minds.

    • Rules or frames are loose and ambiguous.

    • People rely on context to guide their actions.


    • This approach was developed by researchers on a field called “ethnomethodology”.

    • Ethnomethodologists insist that knowledge and understanding are context-dependent (situated).


    • Ethnomethodology studies our taken-for-granted knowledge.

    • One research method is to 'breach' or 'break' the everyday routine of interaction:

      • Pretending to be a stranger in one's own home;

      • Blatantly cheating at board games;

      • Attempting to bargain for goods on sale in stores.

    • This makes explicit the shared regularites that sustains the normal flow of everyday life.


    NOUVELLE AI

    AI without knowledge representation


    Key principles of new AI

    • Cognition-in-practice (situated action)

    • Ecological niche

    • Distributed cognition

    • Emergence

    • Adaptive systems

    • Cheap design

    • Autopoiesis (self-production)


    • Cognition cannot be separated from practical action in some environment (ecological niche).

    • Cognition is not done only in the head: it is distributed over mind, body, and environment.

    • “Cognition observed in everyday practice is distributed—stretched over, not divided among—mind, body, activity and culturally organized settings (which include other actors).” (Jean Leve)

    • “…knowledge-in-practice, constituted in the settings of (social) practice, is the locus of the most powerful knowledgeability of people in the lived-in world.”


    • Cognition-in-action


    • http://www.ace.uci.edu/penny/works/petitmal/petitcode.html


    Emergence

    • Emergence occurs whenever a collection of simple, interacting subunits give rise to new characteristics (known as emergent properties) that are not found in individual subunits.

    • An emergent property is normally the product of collective activity without a central planner or controller.


    Think of an ant colony.

    • Its individual members follow very simple rules.

      • “Take an object”, “Follow a trail” (etc.)

    • The whole colony generates complex patterns on the basis of these simple rules.


    • The colony only exists in virtue of the behavior of its individual members.

    • The colony as a whole, however, is more powerful than its members:

      • It can do things that individual members cannot do (respond to food, enemies, etc.)

      • Lives longer than its members

      • Modifies its environment in ways that individual members cannot.


    • Suppose you want to design robots that collect wood into a pile

    • You can either programme the robot to achieve that purpose (top-down approach).

    • Or you could instead program very simple rules that will yield the desired behavior indidrectly (bottom-up approach).

    • Michael Resnick developed robots that followed simple rules:

      • “Walk around randomly until bumping into a wood chip.”

      • “If you are not carrying anything then pick up the chip.”

      • “If you are carrying wood and bump into another, then put it down.”


    Self-organization

    • This refers to the spontaneous rise and maintenance of order or complexity out of a state that is less ordered.

    • It is not imposed by an external designer or central planner.

    • Order arises out of the internal organization of the system.

    • Resnick’s robots (previous slide) perform a function which has not been directly programmed in them.


    • The flocking behaviors of birds and other animals demonstrate the emergent self-organization of a group acting as a single creature.

    • Flocks develop without a leader.

    • Intelligence here becomes collective rather than individual.

      (“Swarm intelligence”).


    Birds Flocking,

    Sylvia Nickerson

    Collage2004


    SUMBSUMPTION ARCHITECTURE (developed by Rodney Brooks, MIT)

    Example of: distributed cognition, cognition-in-practice, importance of the ecological niche, emergence and self-organization.


    • Brooks faced the usual problem of classical AI:

      How to design a cognitive structure (“mind”) that would control the behavior of the robot.

      Brooks decided to get rid of symbolic cognition.

      No symbolic representation of the world inside the robot.

      Nothing but sense and action.


    “Seeing, walking, navigating, and aesthetically judging do not usually take explicit thought, or chains of thought… They just happen.” (Brooks)

    In insects and other lower animals, sensation and actuation are closely linked, without the intermediary of some internal symbolic representation of the world (by rules, etc.)

    Basic skills are based mainly on the unthinking coordination of perception and action.


    • The key principle is the direct linkage of perception and action.

      • INTELLIGENCE WITHOUT REPRESENTATION


    • Close coupling between sensors and actuators ensures a short reaction time.

    • No need for some representation or plan to control the action.

    • By avoiding world representations, the architecture saves:

      • The time needed to read and write them,

      • The time-cost of algorithms that might employ them

      • The difficulty of keeping up their accuracy.


    • A single robot (agent) is a collection of many Finite State Machines (FSM) augmented with timers.

    • The timers enable state changes after preprogrammed periods of time.

    • Each FSM performs an independent, simple task such as controlling a particular sensor or actuator.

    • These simple actions can produce more complex behavior when they are organized into layers.

    • Each layer implements a recognizable behavior such as wander aimlessly, avoid an obstacle, or follow a moving object.


    For instance, a robot might have three layers:

    1. One layer might ensure that robots avoid colliding with objects.

    2. Another layer would make the robot move around without a fixed goal.

    • Because of the first layer, the second layer has no need to worry about collisions.

      3. A third layer would make it move towards some object sensed in the distance.

    • Because of the first layer, this layer also has no need to worry about clashing with the object.


    • Some layers may inhibit or suppress the behavior of other layers.

    • This method allows different levels to have their own hierarchical "rank of control".


    • The higher layers (or levels of competence) build upon the lower levels to create more complex behaviors.

    • Each higher layer can be built independently and added on to the system to create a higher level of competence.

    • The designer begins by creating the lower layers and then add more and more layers to create more complicated behavior.

    • The behavior of the whole system is the result of many interacting simple behaviors.

    • Simple behaviors are combined in a bottom-up way to form more complex behavior (emergence)


    Distributed intelligence

    • This behavior is distributed:

      • Different FSMs do different tasks that contribute to the overall behavior.

      • The FSMs operate independently of each other without a central control.

      • The timers of the FSMs do not have to synchronize with one another.


    ADAPTIVE SYSTEM

    • No set of rules could possibly prepare a robot for all the events that might happen.

    • In classical AI, unexpected inputs from the environment could trigger a highly inappropriate response.

    • A bottom-up approach, like the subsumption architecture, results in a more flexible and adaptable design.


    • An adaptive system adapts its behavior according to how it senses changes in its environment.

    • Adaptation mainly involves the mutual adjustment of action and environment.

    • It does not necessarily require mental representation.


    Cheap design

    • Computation can be reduced to a very small fraction.

    • Brooks only uses simple sensors, cheap microprocessors, and algorithms with low memory requirements.

    • This is the principle of cheap design: less is more.

    • Since robots are inexpensive, it is possible to create a world populated by many and observe their collective behavior.


    • Each agent is self-contained (autonomous).

      • All computation is performed by the robot.

    • This approach shows that it is possible to design an autonomous agent with a minimal representation of the world.


    The behavior follows from the interaction between organisms and environment.

    It is not controlled only by the internal rules of the organism.


    • A robot might be rather poor at individual tasks, but survive well in a dynamic real-world environment.

    • “Individual behaviors can be composed to compensate for each others failures, resulting in an emergently coherent behavior despite the limitations of the component behaviors.”


    • No need to store all the necessary knowledge, because a lot of the information is simply there in the environment.

    • No need to program every feature of the environment into the robot.

    • We use the interactions between the hardware and the environment (the ecological niche).

    • There is representation of the state of the environment.

    • The robot does not predict all of the effects that its actions will have on the world.

      • The frame problem does not really arise.


    • No longer necessary to assume any complicated internal processing of symbols (drawing inferences, matching representations, retrieving precedents from memory, etc.)

    • Intelligence is no longer “stored” inside the head of the robot.

    • Intelligence is distributed between the robot and its environment (niche).


    • Artist Ken Rinaldo used a version of Brooks’ subsumption architecture.

    • http://www.ylem.org/artists/krinaldo/emergent1.html


    AUTOPOIESIS

    • Autopoiesis literally means "self-production” in Greek.

    • The term was originally introduced by Chilean biologists Francisco Varela and Humberto Maturana in the early 1970s:


    Example of autopoiesis

    The eukaryotic cell is made of various biochemical components (nucleic acids, proteins, etc.), and is organized into bounded structures (the cell nucleus, the organelles, the cell membrane, etc.)

    These structures, thanks to the external flow of molecules and energy, produce the components which continue to maintain the organized structure of the cell.

    It is the structure of the cell that gives rise to these components.

    It is these components that reproduce the cell.

    The biological cell therefore produces itself.


    An autopoietic system is to be contrasted with an allopoietic system.

    • An allopoietic system is “other-producing” rather than “self-producing”.

      A car factory uses raw materials (components) to produce a car (an organized structure) which is something other than itself (a factory).

      The car does not reproduce itself.


    "An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components which:

    • through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and

      (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by specifying the topological domain of its realization as such a network."

      Maturana and Varela


    • Classical AI begins with a task-neutral machine and then devises instructions (programmes) that make the machine carry out a task.

      • Top-down processing.

      • Central planning

    • New AI and A-Life defines very simple rules from which most complex behavior will eventually emerge.

      • Bottom-up processing.

      • Local interactions by simple units.

      • No unit has an overall plan of action.


    CONNECTIONISM


    • An important development in the late 1980s was the use of neural networks.

    • Neural networks are often used to implement the ideas of emergence and self-organization mentioned before.

      Historical note

      The concept of neural networks was already anticipated in the work of the cybernetics movement in the late 40s and 50s.

      In the 60s, however, classical AI became the dominant force. Neural networks were pushed aside…


    • A network is an organization of inter-connected processing units.

    • A neural network is a very large collection of very simple processing units.


    • The term “neural” shows that the original inspiration was the way neurons are connected in the brain.

    • The biological appropriateness of the model, however, is debatable.

    • It is best to understand the model without thinking too much of the biological brain.


    • Key properties of a neural network:

      1. A set of processing units

      2. A pattern of connectivity among these units

      • Network connections are channels through which information flows between members of a network. In the absence of such connections, no group of objects is a network.


    3. An input connection is a conduit through which a member of a network receives information (INPUT).

    4. An output connection is a conduit through which a member of a network sends information (OUTPUT).

    No computer belongs to a network unless it can receive information (INPUT) from other computers or send information (OUTPUT) to other computers.


    • A processing unit is roughly analogous to a neuron in the brain.

    • In the brain, information flows from neuron to neuron through the synapses.


    • In a neural network, the flow of information is often organized into layers.


    • In this example, every unit is connected to all the units above it.

    • This is called a three-layered feedforward network.


    • The input (signals received by) a unit are called activation values (or simply activations).

    • An activation value is a number.


    • The activation value is normally between 0 and 1.

    • This number indicates how active the unit is.


    • A unit typically receives activation values from several other input units.

    • The unit computes its own activation value depending on the activation values it receives from the input units.


    • The unit then sends its activation value to other units, thus helping to transmit information through the net.


    • The output of a unit depends on its inputs.

    • It also depends on something called its connection weight (or just “weight”).


    • Weights may be positive or negative.

      • They usually range from -1 to 1.

    • Weights represent the strength of a connection.

      • A positive weight is a stronger connection than a negative weight.

      • A negative weight is a weaker connection.


    • A unit receives many incoming signals.

    • It must compute its combined input before it can process its output.


    • The COMBINED INPUT to a unit is the sum of each INPUT activation multiplied by its connection weight.


    • The activation function of a unit ensures that its output will never exceed an acceptable range (maximum or minimum).

    • For example, if the acceptable range is 0 to 1, then the value of the combined input must be translated into a number between 0 and 1.

    • This value is the output activation of the unit.


    • Neural networks tend to be massively parallel.


    • Neural nets resemble the brain in two ways:

      • Distribution

        The execution of particular tasks is often distributed over several brain regions. Functions are not always localized in a specific physical area of the brain.

      • Parallelism.

        Brain activity is not serial but vastly parallel.

    • Connectionist models of computation combine these two ideas.

      • The model is often also called parallel distributed processing (PDP).


    • The simple net we have discussed is called a feed forward net.

    • Activation flows directly from inputs to hidden units and then on to the output units.

    • More complex models include many layers of hidden units, and recurrent connections sending signals backwards.


    • Connectionism is another name for the use of neural nets in AI.

    • Connectionism is also a cognitive theory.

      • “Thinking” can be explained by collections of units that operate in this way in the brain.


    • All the units calculate roughly the same (very simple) activation function.

    • The operation of the network to a large extent depends on the weights between the units.

    • The goal of connectionist research involves finding the right weights between units.


    • Here is one method:

      1. Suppose we want a net to carry out some task (such as recognizing male and female faces in a picture).

      2. The net might have two output units (indicating the “male” and “female”) and many input units, one devoted to the brightness of each pixel in the picture.


    3. The weights of the net to be trained are initially set to random values.

    4. The net is then “shown” some picture(s).

    5. The actual output of the net is compared with the desired output.

    6. Every weight in the net is modified slightly to bring the net's actual output values closer to the desired output values.


    7. The process is repeated until the desired output values are produced at the appropriate times.

    8. The ideal objective is to let the net “generalize” its behavior, so as to “recognize” even male and female faces it has never “seen” before.

    To “recognize” something is to send an appropriate output when confronted with that something.


    • Thus a neural network can be said to “learn”.

      Its acquired ability is an emergent property or characteristic of the network.

    • An emergent characteristic is the characteristic of a whole (such as a network) which cannot be predicted from any knowledge of its parts (the processing units).


    • Connectionists no longer need to program all the knowledge into the computer by using explicit symbols.

    • The computer evolves the knowledge.

    • There is no need to program a particular plan, script, or frame into the computer.


    Some tasks that neural networks can do:

    • Pronounce some English text.

    • Recognize the tenses of verbs.

    • Recognize other grammatical structures and construct correct sentences.

    • Recognize shapes

    • Recognize speech.


    • Many definitions have exceptions.

    • Philosophers and psychologists believe that concepts have flexible boundaries.

      • Concepts do not always have clear-cut membership conditions.

    • Connectionist models seem especially suitable to taken into account the flexibility and ambiguity of concepts.


    Distributed representation

    • Connectionist models have been used to tackle the question:

      How does the brain represent information?


    • It is not true that an individual neuron or a small chunk of neurons (a node in the net) represents one thought (for instance, our memory of a particular place or the concept “dog”).

    • Instead, every thought is represented by a complex pattern of activity across various parts of the brain.

    • Representation is distributed rather than local.


    • Each representation involves many units

    • Each unit participates in many representations.


    Connectionism vs. classical AI

    • Classical AI involved systems which use explicit logical principles, rules, scripts, frames, or similar symbolic structures.

    • It often used rules with conditions and actions.

    • Classical AI relied on symbolic representation.


    • Instead of symbols stored in the brain (the classical idea of knowledge representation in AI), cognitive representation involves activation patterns distributed throughout the brain.

    • "Information is not stored anywhere in particular. Rather it is stored everywhere. Information is better thought of as 'evoked' than 'found'" (Rumelhart & Norman 1981).


    • Whereas classical AI emphasized symbolic representation, connectionist representation is sub-symbolic.

      • Connectionism works on cognitive microstructures.

    • Connectionist systems involve the massively parallel processing of sub-symbols


    • Neural networks can be used to represent traditional logical relations.

    • Suppose that node y will only be active when its input value is at least 1.


    • But neural nets are often used in a manner very different from classical AI. This is the emphasis of today’s lecture.


    • Connectionism has influenced the development of a philosophical viewpoint known as ELIMINATIVE MATERIALISM.

      Note: A psychologist or computer science who works with neural networks does not necessarily have to support Eliminative Materialism! Many of them do not!


    Eliminative materialism (E. M.)

    • This strong version of materialism was defended by Paul and Patricia Churchland.

    • They do not say that mental processes are the same as brain processes.

      • They say that mental processes do not exist.

      • Descriptions of desires, emotions, sensations, etc. are empty.

      • They do not refer to anything that exists.


    • All that really exists are patterns of neural activation in the brain.


    Comparison of E. M. and Functionalism

    • Functionalism attempts to explain mental states.

    • E. M. claims that mental states are an illusion.

    • They should not be explained, but “eliminated” from the theory.


    • Most of us explain one another’s actions by speaking of “beliefs”, “emotions” and “desires”.

    • This commonsense theory of the mind is called FOLK PSYCHOLOGY.

    • According to eliminative materialism, folk psychology is all wrong.


    • According to E. M.,

      …folk psychology will be completely displaced by a true theory of the brain.


    • In any case, we need not accept EM to see that connectionism is a powerful model of AI.


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