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AI Philosophy. AI Philosophy. Presentation Transcript

  • AI Philosophy: Computers and Their Limits G51IAI – Introduction to AI Andrew Parkes
  • 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?
  • Turing Test
    • The 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: Modern
    • You’re on the internet and open a chat line (modern teletype) to two others “A” and “B”
    • Out of A and B
      • one is a person
      • one is a machine trying to imitate a person (e.g. capable of discussing the X-factor?)
    • If you can’t tell the difference then the machine must be intelligent
    • Or at least act intelligent?
  • Turing Test
    • Often “forget” the second person
    • Informally, the test is whether the “machine” behaves like it is intelligent
    • This is a test of behaviour
    • It is does not ask “does the machine really think?”
  • Turing Test Objections
    • It 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 Room
    • The system comprises:
      • a human, who only understands English
      • a rule book, written in English
      • two stacks of paper.
        • One stack of paper is blank.
        • The other has indecipherable symbols on them.
    • In computing terms
      • the human is the CPU
      • the 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: Process
    • The 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: Summary
    • Simple Rule processing system but in which the “rule processor” happens to be intelligent but has no understanding of the rules
    • The set of rules might be very large
    • But this is philosophy and so ignore the practical issues
  • Searle’s Claim
    • We 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 Searle
    • The Systems Reply
    • The Robot Reply
    • The 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-Vat
    • The 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 Terminology
    • “ Weak AI”
      • machine can possibly act intelligently
    • “ Strong AI”
      • machines can actually think intelligently
    • AIMA: “Most AI researchers take the weak hypothesis for granted, and don’t 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, etc
    • But does it matter “in theory”?
  • Turing Machine
    • A very simple computing device
      • storage: a tape on which one can read/write symbols from a list
      • processing: a “finite state automaton”
  • Turing Machine: Storage
    • Storage: a tape on which one can read/write symbols from some fixed alphabet
      • tape is of unbounded length
        • you never run out of tape
      • have the options to
        • move to next “cell” of the tape
        • read/write a symbol
  • Turing Machine: Processing
    • “finite state automaton”
      • The processor can has a fixed finite number of internal states
      • there are “transition rules” that take the current symbol from the tape and tell it
        • what to write
        • whether to move the head left or right
        • which state to go to next
  • Turing Machine Equivalences
    • The 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 Machine
    • This is fixed machine that can simulate any other Turing machine
      • the “program” for the other TM is written on the tape
      • the UTM then reads the program and executes it
    • C.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 computing
      • then 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 other
      • as long as have enough time and space then computers can all emulate each other
      • an operating system of 2070 will still be able to run a 1980’s .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 principle
      • best-known example uses program termination:
  • Program Termination
    • Prog 1:
      • i=2 ; while ( i >= 0 ) { i++; }
    • Prog 2:
      • i=2 ; while ( i <= 10 ) { i++; }
    • Prog 1 never halts(?)
    • Prog 2 halts
  • Program Termination
    • Determining program termination
    • Decide whether or not a program – with some given input – will eventually stop
      • would seem to need intelligence?
      • would exhibit intelligence?
  • Halting Problem
    • 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 eventually
      • i.e. it must always be able to answer true/false to “P halts on I”
  • Halting Problem
    • INPUT: the code for a program P, and an input I
    • OUTPUT: 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 Problem
    • TURING 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 basically
      • “a symbol-pushing system can be intelligent”
    • For the “symbol manipulation” let’s consider a “formal system”:
  • “ Formal System”
    • Consists of
    • Axioms
      • statements taken as true within the system
    • Inference rules
      • rules used to derive new statements from the axioms and from other derived statements
    • Classic Example:
    • Axioms:
      • All men are mortal
      • Socrates is a man
    • Inference Rule: “if something is holds ‘for all X’ then it hold for any one X”
    • Derive
      • Socrates is mortal
  • Limits of Formal Systems
    • Systems can do logic
    • They have the potential to act (be?) intelligent
    • What can we do with “formal systems”?
  • “ Theorem Proving”
    • Bertrand Russell & Alfred Whitehead
    • Principia Mathematica 1910-13
    • Attempts to derive all mathematical truths from axioms and inference rules
    • Presumption was that
      • all mathematics is just
        • set up the reasoning
        • then “turn the handle”
    • Presumption was destroyed by Gödel:
  • Kurt G ö del
    • Logician, 1906-1978
    • 1931, Incompleteness results
    • 1940s , “invented time travel”
      • demonstrated existence of &quot;rotating universes“, solutions to Einstein's general relativity with paths for which ..
      • “ on doing the loop you arrive back before you left”
    • Died of malnutrition
  • Gödel's Theorem (1931)
    • Applies to systems that are:
    • formal:
      • proof is by means of axioms and inference rules following some mechanical set of rules
      • no external “magic”
    • “ consistent”
      • there is no statement X for which we can prove both X and “not X”
    • powerful enough to at least do arithmetic
      • the system has to be able to reason about the natural numbers 0,1,2,…
  • Gödel's Theorem (1931)
    • In consistent formal systems that include arithmetic then
    • “ There are statements that are true but the formal system cannot prove”
    • Note: it states the proof does not exist, not merely that we cannot find one
    • Very few people understand this theorem properly
      • I’m not one of them 
      • I don’t expect you to understand it either! …
      • just be aware of its existence as a known limit of what one can do with one kind of “symbol manipulation”
  • Lucas/Penrose Claims
    • Book: “Emperor's New Mind” 1989 Roger Penrose, Oxford Professor, Mathematics
    • (Similar arguments also came from Lucas, 1960s)
    • Inspired by G ö del’s Theorem:
      • Can create a statement that they can see is true in a system, but that cannot be shown to be true within the system
    • Claim: we are able to show something that is true but that a Turing Machine would not be able to show
    • Claim: this demonstrates that the human is doing something a computer can never do
    • Generated a lot of controversy!!
  • Penrose Argument
    • Based on the logic of the G ö del’s Theorem
    • That there are things humans do that a computer cannot do
    • That humans do this because of physical processes within the brain that are noncomputable, i.e. that cannot be simulated by a computer
      • compare to “brain in a vat” !?
    • Hypothesis: quantum mechanical processes are responsible for the intelligence
    • Many (most?) believe that this argument is wrong
  • Penrose Argument
    • Some physical processes within the brain are noncomputable, i.e. cannot be simulated by a computer (UTM)
    • These processes contribute to our intelligence
    • Hypothesis: quantum mechanical and quantum gravity processes are responsible for the intelligence (!!)
    • (Many believe that this argument is wrong)
  • One Reply to Penrose
    • Humans are not consistent and so Gödel's theorem does not apply
    • Penrose Response:
      • In the end, people are consistent
      • E.g. one mathematician might make mistakes, but in the end the mathematical community is consistent and so the theorem applies
  • Summary
    • Church-Turing Hypothesis
      • all known computers are equivalent in power
      • a simple Turing Machine can run anything we can program
    • Physical Symbol Hypothesis
      • intelligence is just symbol pushing
    • There are known limits on “symbol-pushing” computers
      • halting problem, Gödel’s theorem
    • Penrose-Lucas: we can do things symbol pushing computers can’t
      • Some “Turing Tests” will be failed by a computer
      • Some tasks cannot be performed by a “Chinese room”
      • but the argument is generally held to be in error
  • Questions?