Jan 21, 2016

AI Philosophy: Computers and Their Limits. G51IAI – Introduction to AI Andrew Parkes http://www.cs.nott.ac.uk/~ajp/. Natural Questions. Can a computer only have a limited intelligence? or maybe none at all? Are there any limits to what computers can do? What is a “computer” anyway?. - PowerPoint PPT Presentation

AI Philosophy:Computers and Their LimitsG51IAI Introduction to AIAndrew Parkeshttp://www.cs.nott.ac.uk/~ajp/

Natural QuestionsCan a computer only have a limited intelligence? or maybe none at all?Are there any limits to what computers can do?What is a computer anyway?

Turing TestThe test is conducted with two people and a machine.One person plays the role of an interrogator and is in a separate room from the machine and the other person.The interrogator only knows the person and machine as A and B. The interrogator does not know which is the person and which is the machine.Using a teletype, the interrogator, can ask A and B any question he/she wishes. The aim of the interrogator is to determine which is the person and which is the machine.The aim of the machine is to fool the interrogator into thinking that it is a person. If the machine succeeds then we can conclude that machines can think.

Turing Test: ModernYoure on the internet and open a chat line (modern teletype) to two others A and B Out of A and B one is a personone is a machine trying to imitate a person (e.g. capable of discussing the X-factor?)

If you cant tell the difference then the machine must be intelligentOr at least act intelligent?

Turing TestOften forget the second personInformally, the test is whether the machine behaves like it is intelligentThis is a test of behaviourIt is does not ask does the machine really think?

Turing Test ObjectionsIt is too culturally specific?If B had never heard of The X-Factor then does it preclude intelligence? What if B only speaks Romanian?Think about this issue!

It tests only behaviour not real intelligence?

Chinese RoomThe system comprises:a human, who only understands Englisha rule book, written in Englishtwo stacks of paper. One stack of paper is blank. The other has indecipherable symbols on them.In computing terms the human is the CPUthe rule book is the program the two stacks of paper are storage devices. The system is housed in a room that is totally sealed with the exception of a small opening.

Chinese Room: ProcessThe human sits inside the room waiting for pieces of paper to be pushed through the opening. The pieces of paper have indecipherable symbols written upon them. The human has the task of matching the symbols from the "outside" with the rule book. Once the symbol has been found the instructions in the rule book are followed. may involve writing new symbols on blank pieces of paper,or looking up symbols in the stack of supplied symbols. Eventually, the human will write some symbols onto one of the blank pieces of paper and pass these out through the opening.

Chinese Room: SummarySimple Rule processing system but in which the rule processor happens to be intelligent but has no understanding of the rulesThe set of rules might be very largeBut this is philosophy and so ignore the practical issues

Searles ClaimWe have a system that is capable of passing the Turing Test and is therefore intelligent according to Turing. But the system does not understand Chinese as it just comprises a rule book and stacks of paper which do not understand Chinese.Therefore, running the right program does not necessarily generate understanding.

Replies to SearleThe Systems Reply The Robot ReplyThe Brain Simulator Reply

Blame the System!The Systems Reply states that the system as a whole understands.Searle responds that the system could be internalised into a brain and yet the person would still claim not to understand chinese

Make Data?The Robot Reply argues we could internalise everything inside a robot (android) so that it appears like a human. Searle argues that nothing has been achieved by adding motors and perceptual capabilities.

Brain-in-a-VatThe Brain Simulator Reply argues we could write a program that simulates the brain (neurons firing etc.)Searle argues we could emulate the brain using a series of water pipes and valves. Can we now argue that the water pipes understand? He claims not.

AI TerminologyWeak AImachine can possibly act intelligently

Strong AImachines can actually think intelligently

AIMA: Most AI researchers take the weak hypothesis for granted, and dont care about the strong AI hypothesis (Chap. 26. p. 947)

What is your opinion?

What is a computer?In discussions of Can a computer be intelligent?Do we need to specify the type of the computer?Does the architecture matter? Matters in practice: need a fast machine, lots of memory, etcBut does it matter in theory?

Turing MachineA very simple computing devicestorage: a tape on which one can read/write symbols from a listprocessing: a finite state automaton

Turing Machine: StorageStorage: a tape on which one can read/write symbols from some fixed alphabettape is of unbounded length you never run out of tapehave the options to move to next cell of the taperead/write a symbol

Turing Machine: Processingfinite state automaton The processor can has a fixed finite number of internal statesthere are transition rules that take the current symbol from the tape and tell it what to writewhether to move the head left or rightwhich state to go to next

Turing Machine EquivalencesThe set of tape symbols does not matter!

If you have a Turing machine that uses one alphabet, then you can convert it to use another alphabet by changing the FSA properly

Might as well just use binary 0,1 for the tape alphabet

Universal Turing MachineThis is fixed machine that can simulate any other Turing machinethe program for the other TM is written on the tapethe UTM then reads the program and executes itC.f. on any computer we can write a DOS emulator and so read a program from a .exe file

Church-Turing Hypothesis

All methods of computing can be performed on a Universal Turing Machine (UTM)

Many computers are equivalent to a UTM and hence all equivalent to each other

Based on the observation that when someone comes up with a new method of computingthen it always has turned out that a UTM can simulate it,and so it is no more powerful than a UTM

Church-Turing Hypothesis

If you run an algorithm on one computer then you can get it to work on any otheras long as have enough time and space then computers can all emulate each otheran operating system of 2070 will still be able to run a 1980s .exe file

Implies that abstract philosophical discussions of AI can ignore the actual hardware?or maybe not? (see the Penrose argument later!)

Does a Computer have any known limits?Would like to answer: Does a computer have any limit on intelligence?

Simpler to answer Does a computer have any limits on what it can compute?e.g. ask the question of whether certain classes of program can exist in principlebest-known example uses program termination:

Program TerminationProg 1: i=2 ; while ( i >= 0 ) { i++; }

Prog 2:i=2 ; while ( i

Program TerminationDetermining program termination Decide whether or not a program with some given input will eventually stopwould seem to need intelligence?would exhibit intelligence?

Halting ProblemSPECIFICATION: HALT-CHECKER

INPUT: 1) the code for a program P 2) an input I

OUTPUT: determine whether or not P halts eventually when given input I return true if P halts on I, false if it never halts

HALT-CHECKER itself must always halt eventuallyi.e. it must always be able to answer true/false to P halts on I

Halting ProblemSPECIFICATION: HALT-CHECKERINPUT: the code for a program P, and an input IOUTPUT: true if P halts on I, false otherwise

HALT-CHECKER could merely run P on I?If P halts on I then eventually it will return true; but what if P loops on I?BUT cannot wait forever to say it fails to halt!Maybe we can detect all the loop states?

Halting ProblemTURING RESULT: HALT-CHECKER (HC) cannot be programmed on a standard computer (Turing Machine)it is noncomputable

Proof: Create a program by feeding HALT-CHECKER to itself and deriving a contradiction (you do not need to know the proof)

IMPACT: A solid mathematical result that a certain kind of program cannot exist

Other Limits?Physical System Symbol Hypothesis is basicallya symbol-pushing system can be intelligent

For the symbol manipulation lets consider a formal system:

Formal SystemConsists ofAxioms statements taken as true within the systemInference rulesrules used to derive new statements from the axioms and from other derived statements

Classic Example:Axioms:All men are mortalSocrates is a manInference Rule: if something is holds for all X then it hold for any one XDerive Socrates is mortal

Limits of Formal SystemsSystems can do logicThey have the potential to act (be?) intelligent

What can we do with formal systems?

Theorem ProvingBertrand Russell & Alfred Whitehead Principia Mathematica 1910-13Attempts to derive all mathematical truths from axioms and inference rulesPresumption was that all mathematics is justset up the reasoningthen turn the handlePresumption was destroyed by Gdel:

Kurt GdelLogician, 1906-19781931, Incompleteness results1940s, invented time traveldemonstrated existence of "rotating universes, solutions to Einstein's general relativity with paths for which ..on doing the loop you arrive back before you leftDied of malnutrition

Gdel's Theorem (1931)Applies to systems that are:formal:proof is by means of axioms and inference rules following some mechanical set of rulesno external magic consistent there is

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