can machines think? seminar by annervaz (07305063) jaideep (06305r01) k.v.m.v kiran (04005031) ...

CAN MACHINES THINK?

Seminar by Annervaz (07305063) Jaideep (06305R01) K.V.M.V Kiran (04005031) L. Srikanth (04005029) Vasudevan (06405004)

“I propose to consider the question, 'Can machines think?' ”

-Alan Turing

Motivation

Computers today capable of doing task which were previously thought to be exclusively in human domain

Any limitation to machine's capability?

Can machine do everything that human brain can do?

Machine “Intelligence” <=> Human Intelligence

Hot debate in AI community

Outline

Introduction

Can Machines Think?

Imitation game – Turing test

Proponents and opponents of TT

Introduction to interactive proof

TT as Interactive proof

Conclusion

“can” “machines” “think”

“can”

Theoretically possible?

Practically realizable?

“machines”

Every engineering technique permitted

Manner of operation need not be completely known

“think”

“thinking is as thinking does”

Intelligence necessary and sufficient for thinking

Intelligence (contd...)

“Intelligence” - Based on action:

Rational action: Act to achieve best (possible) outcome,

given what one knows

Human actions:Turing Test designed to measure this

Intelligence...(contd)

Based on thinking: Rational thinking:Irrefutable reasoning process; argument

structures that always yield correct conclusions given correct premises

Human thinking: studied in cognitive science which attempts to combine AI and experimental techniques from psychology

Artificial Intelligence: when an entity other than a natural life form possesses

“intelligence”

Outline

Introduction

Can Machines Think?





conclusion

Can Machines Think?Mathematical Objection

Gödel's Theorem

Gödel's Theorem

• Any sufficiently powerful consistent axiomatic system is necessarily incomplete in that there will always be statements that can neither be proved nor disproved from their axioms.

• Corollary:- No sufficiently powerful formal system is powerful enough to prove its own consistency

Gödel's Theorem – Proof Outline

The key idea is to construct a proposition P which asserts “P is not provable”

P is neither provable nor disprovable, as both leads to

contradiction

If P were false, P would be provable

If P were true, P is not provable

Implications of Gödel's Theorem

• Roger Penrose’s claim: “Human mathematicians are not using a knowably

sound algorithm in order to ascertain mathematical truth”.

If they were, it would constitute an algorithm which

can assert it’s own soundness which Gödel’s theorem proves is impossible.

Implications of Gödel's Theorem

• People seem to simply be able to “see” the truth of some statements (“intuition” and “insight”)

• Provability is a weaker notion than truth

• Lucas Argument

• “Some Gödel statements, the machine will be unable to produce as true, although a mind can see that it is true. And so the machine will not be an adequate model of the mind ”

Counter arguments

• Even humans fallible to Gödel's theorem

• “Lucas cannot prove this statement”

• Every human other than Lucas can see this statement is true

• But Lucas can never prove this, from just being ‘inside’ his ‘system’.

• Mind may be exhibiting ‘rational’ inconsistency,and thereby being a formal system consistent with Gödel's theorem

Can Machines Think?Consciousness Objection

Arguments

no mechanism can feel: Anger, grief, warmth, pleasure

Counter Arguments

What is feeling?

Machine can have its own set of feelings.

Aren't external actions enough?

Can Machines Think?Lady Lovelace Objection

Arguments

Machine is deterministic

Machine cannot originate anything

Counter Arguments Learning Machines

Low level determinism does not imply high level

predictable behavior

Can Machines Think?Continuity vs. discreteness

Arguments

Nervous system is continuous

Discrete state system like digital computer can't simulate

nervous system

Counter arguments:

Why can real thought be located only in continous-state

system?

Discrete-state system may still be intelligent

Church-Turing Hypothesis

Can Machines Think?Theological Objection

Arguments

Thinking is a part of Human soul

Man is made in gods own image

Intelligent machine can be a threat to humans

Counter Arguments

Why gods image cannot be passed on?

Why be so pessimistic and selfish?

Outline

Introduction

Can Machines think?





conclusion


Objective: Interrogator determines which is man and

which is woman

B: tries to help C

A: tries and cause C to make the wrong


Replace A with machine

Will the interrogator decide wrongly as often as earlier?

This replaces 'Can Machines think?'

Practical version: “Will an average interrogator have

more than, say 70% chance, of making the right

identification after 5min of questioning?”

Turing Test

Test of adequacy of an agent's verbal behavior

TT is based on the idea that ability to produce sensible

verbal response is intelligence

Tests the “human action” part of intelligence

Can be theoretically formulated as below-

Turing Test(contd..)

Premise 1:If an agent passes a TT, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli.

Premise 2: If an agent produces a sensible sequence

of verbal response to a sequence of verbal stimuli, then

it is intelligent.

Conclusion:Therefore, if an agent passes TT then it is

intelligent.

Outline

Introduction

Machines can't think

Counter arguments - 'machines can think !'





conclusion

Opponents of Turing Test

It is widely agreed that TT is not a necessary condition for intelligence.

Any machine would require sensory organs and

sociological training to pass TT: very difficult task even

for an “intelligent” machine.

TT is of little value in guiding actual AI research

Total test: should involve responding to all inputs, not

just verbal

Block's Argument

TT merely tests behavior

TT is silent about internal working.

Memorizing machine: machine that stores sensible

responses to all possible sequences of verbal inputs

Practically infeasible but possible in principle

Such a machine does not fit into our concept of “intelligence”

So TT is not a sufficient condition for intelligence

Some extra-conditions on the working of the machine are

required

Proponents-Stuart's argument

TT a sufficient condition for intelligence!

logically necessary for intelligence

Extra conditions can be revealed by a TT

“Slight weakening” of proof criterion required

Weakening: Statistical Proof instead of a logical one

Weakening makes no conceivable difference from a

practical standpoint

TT Rephrased

Premise 1:

If an agent passes k rounds of a TT of at least one

minute in length, then (with a prob. of error exponentially

small in k) it has a capacity to produce a sensible

sequence of verbal responses to a sequence of verbal

stimuli that is logarithmic in the storage capacity of the

agent, whatever they may be.

TT Rephrased (continued...)

Premise 2:

If an agent has the capacity to produce a sensible



agent, whatever they may be, then it is intelligent.

Conclusion:

If an agent passes k rounds of a TT of at least 1 minute

in length (with probability of error exponentially small in k)

it is intelligent

Outline

Introduction







conclusion

Interactive proof System

An interactive proof system is an abstract machine that models computation as the exchange of messages between two parties

Prover, P having unlimited computation power

Verifier, V with polynomially bounded computation power

Assertion 's'

Randomization and Interaction

Multiple rounds of message-passing

Interactive Proof Examplegraph non-isomorphism

Graph Isomorphism – if there is any edge between any two vertices in first graph, then there should be an edge in between corresponding vertices in other graph

Given graphs G0 and G

1

P's assertion s

G0 and G

1 are NOT isomorphic

Interactive Proof example(s:Graphs G

0&G

1 are Not Isomorphic)

P(bit – b')[infinite resources]

b'=0 If Isomorphic(G0,G') b'=1 otherwise Send b' to V

V(bit – b)[limited resources]

b = rand(0,1) [Prob=0.5] G' = random permute(G

b)

Send G' to P

s: proved, if b==b'

Interactive Proof Example(continued...)

V selects Gb randomly, b=0 or 1

V does a random permutation G' of Gb

V sends G' to P

P checks if G' isomorphic to G0.

If so,sends back b' = “0”, else b' = “1”

V checks if b=b'. If so, V accepts proof- assertion proved

else V rejects proof

Interactive Proof ExampleGraph Non-Isomorphism

If G0 and G

1 are isomorphic, then clue provides no help in guessing

the number Prover guesses randomly, being wrong about half the time Probability of false positive after k rounds is 1 in 2k.

B Truth value of assertion B' Conclusion about assertion

0 True(not isomorphic) 0 True(not isomorphic)

1 True(not isomorphic) 1 True(not isomorphic)

0 False(isomorphic) 0 True(not isomorphic)

1 False(isomorphic) 0 False(isomorphic)

Outline

Introduction







conclusion

TT As Interactive Proof

capacity conception If an agent has the capacity to produce a sensible

sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, then it is intelligent

generalizability compactness conception

If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, without requiring storage exponential in the length of the sequence,then it is intelligent

logarithmic storage

TT As Interactive Proofcapacity

P: Computer

V: Interrogator

assertion s: “P has the capacity to produce sensible


stimuli, whatever they may be”


space: all possible verbal stimuli sequences

tp: fraction of space for which P can perform correctly

tl: lower bound of tp for acceptance

if tp>tl then P has general capacity


select sample (size K) uniformly

t: fraction of sample for which P can perform correctly

ts: lower bound of t for passing


false positive t

p<t

l and t>t

s

Pr[t>ts] < e-ck, using Chernoff bounds

Pr(false positive) decrease exponentially with k

Choice of ts,t

l does not change basic natue of argument

Similarly, Pr(false negative) decreases exponentially with

k

TT As Interactive Proofcompactness

length of sequence is greater than logarithm of storage capacity

By Quantum theory and bounded volume of universe,

information capacity of universe estimated to be 10185

Turing Test of less than 1 min enough to judge

Above “Critical TT length” too short? Counter-intuitive?

TT As Interactive Proofcompactness

Reasons for short TT length requirement: TT unrestricted; all queries of any sort on any topic

allowed. Machine we wish to unmask is of a particular sort- one

that has memorized answers to every possible such query

In IP samples are independent. Here, judge free to use knowledge from previous responses Only reduces probability of error

Properties of IP and TT

non transferability

provide proof only to verifier

lack of closure under composition

fails under composition

What we Proved

Premise 1:

If an agent passes k rounds of a TT of at least one

minute in length, then (with a prob. of error exponentially

small in k) it has a capacity to produce a sensible



agent, whatever they may be.

What we proved

Premise 2(modified compactness conception-based):

If an agent has the capacity to produce a sensible



agent, whatever they may be, then it is intelligent.

Conclusion: If an agent passes k rounds of a TT of at least 1 minute

in length (with probability of error exponentially small in k) it is intelligent

Conclusions

Varied definitions of intelligence, AI Not much consensus among experts on how to

determine or measure it Numerous attempts made to define and measure-

scientists,philosophers, engineers One such attempt, TT quite popular and proved with

slight weakening to be sufficient for intelligence. AI has influenced and has been influenced by various

other fields. The debate has both inspired as well as distracted from

research of practical value

References

Block, N. 1981. Psychologism and behaviorism. Philosophical Review XC(1):5-43.

Dennett, D. C. (1985) Can machines think? In: How we know, ed. M.

Shafto, Harper and Row.

Harnad, Stevan. (2006) The Annotation Game: On Turing (1950) on

Computing, Machinery, and Intelligence.

Hofstadter, Douglas R. (1999), Gödel, Escher, Bach, Basic Books.

James H. Moor. An analysis of the Turing test. Philosophical Studies,

30:249-257, 1976.

References

Stalker, D. (1978), ‘Why Machines Can’t Think: A Reply to

James Moor’, Philosophical Studies 34, pp. 317-320.pp. 317–320.

Shieber, S. M. To appear. The Turing test as interactive proof,

Nous.

Stuart M. Shieber 2006. Does the Turing Test Demonstrate

Intelligence or Not? In Proceedings of the Twenty-First National

Conference on Artificial Intelligence (AAAI-2006), Boston,

MA,16-20 July.

Turing, A. (1950), ‘Computing Machinery and Intelligence’, Mind

59(236), pp. 433–460.

can machines think? seminar by annervaz (07305063) jaideep (06305r01) k.v.m.v kiran (04005031) ...

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