## Towards a theory of intelligence

Venue: | Theoretical Computer Science |

Citations: | 3 - 1 self |

### BibTeX

@ARTICLE{Kugel_towardsa,

author = {Peter Kugel},

title = {Towards a theory of intelligence},

journal = {Theoretical Computer Science},

year = {},

pages = {2004}

}

### OpenURL

### Abstract

In 1950, Turing suggested that intelligent behavior might require “a departure from the completely disciplined behaviour involved in computation”, but nothing that a digital computer could not do. In this paper, I want to explore Turing’s suggestion by asking what it is, beyond computation, that intelligence might require, why it might require it and what knowing the answers to the first two questions might do to help us understand artificial and natural intelligence.

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Citation Context ... often called induction. (We see a hundred swans, all of which are white, and infer, by induction, that “All swans are white.”) I am going to try to characterize what we might call, following Chomsky =-=[5]-=-, the abstract competence that underlies this process rather than what he called the concrete performance. So I am going to assume, among other things, that the inputs to the learner are error-free an... |

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Citation Context ...ry and intelligence. He changed his mind before he got very far when he realized that, although he had a precise definition of “computing machinery”, in terms of what we now call the “Turing machine” =-=[22]-=-, he lacked a precise definition of “intelligence”. So, instead of discussing intelligence, he changed the subject [15] and discussed what he called the “imitation game” [26] instead 1 . If we try to ... |

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Citation Context ...estions might do to help us understand artificial and natural intelligence. Keywords: intelligence; artificial intelligence; hypercomputers; super-recursive algorithms 1. Introduction In 1950, Turing =-=[26]-=- wrote a famous paper in which he planned to discuss the relationship between computing machinery and intelligence. He changed his mind before he got very far when he realized that, although he had a ... |

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Citation Context ...t a time. It might for example, run several sub-learners, each using a different strategy to acquire programs. It could then (somehow) choose the best result that any sub-system came up with. Gardner =-=[8]-=- has suggested that human intelligence may come in different “flavors” or “intelligences”, each suited to a different domain. Given a particular problem, the mind might set several of these intelligen... |

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Citation Context ...order to talk about such oracles, I will denote the sequence consisting of all ones by “1*” and, more generally, the sequence that consists of the infinite repetition of the finite sequence s by “s*” =-=[13]-=-. I will denote the sequence that consists of n repetitions of s by “s n ”, the first n symbols of s by “ns” and the result of concatenating one sequence, s, to another, t, by “st”.) Before looking at... |

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Citation Context ...A limiting-computable learner can cover the set of all Zog-fa’s Proof. A limiting-computable learner can do this using what has come to be known as an enumeration method (Gold [10], Angluin and Smith =-=[1]-=-). An enumeration method uses a sub-program that generates a list of totally computable programs (a1, a2, a3,…) such that, for any machine in the domain, there is at least one program in the list that... |

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Citation Context ...ncement condition can execute what Burgin [3] has called superrecursive algorithms – algorithms that can evaluate uncomputable functions. In particular they can execute limiting-computable algorithms =-=[10, 19]-=-. The distinction between what we might call recursive computing (which is the traditional kind) and limiting computing (which is one kind of super-recursive computing) can be stated quite simply. Whe... |

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Citation Context ...ncement condition can execute what Burgin [3] has called superrecursive algorithms – algorithms that can evaluate uncomputable functions. In particular they can execute limiting-computable algorithms =-=[10, 19]-=-. The distinction between what we might call recursive computing (which is the traditional kind) and limiting computing (which is one kind of super-recursive computing) can be stated quite simply. Whe... |

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Citation Context ...ne case where this seems to be the case. The human brain seems to have one module for thinking about (and therefore, presumably, learning about) inanimate objects and another for dealing with humans. =-=[20]-=- These two modules seem to be physically distinct and therefore could use different algorithms. If the theory I am proposing here makes sense, we should expect to see more such modules in the brain. F... |

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Citation Context ...he arithmetic hierarchy [12]. It is hard to see how we could use hypercomputers in place of super-recursive algorithms for this purpose. Although hypercomputers (such as the neural nets of Siegelmann =-=[21]-=- or the quantum computers of Kieu [11]) can evaluate super-recursive algorithms, their ability to do so assumes that all the data they will need is potentially available at the start. This allows them... |

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Citation Context ...rd to see how we could use hypercomputers in place of super-recursive algorithms for this purpose. Although hypercomputers (such as the neural nets of Siegelmann [21] or the quantum computers of Kieu =-=[11]-=-) can evaluate super-recursive algorithms, their ability to do so assumes that all the data they will need is potentially available at the start. This allows them (in theory) to solve such classical p... |

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Citation Context ...al and error” machines [14]. A more general, and more abstract, discussion of such procedures in logical, rather than machine, terms can be found in Kleene’s classic paper on the arithmetic hierarchy =-=[12]-=-. It is hard to see how we could use hypercomputers in place of super-recursive algorithms for this purpose. Although hypercomputers (such as the neural nets of Siegelmann [21] or the quantum computer... |

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Citation Context ...y powerful enough to produce intelligent behavior [26]. In other words, intelligence does not require any new, morepowerful, hardware. (In other words, it does not require what Copeland and Proudfoot =-=[6]-=- have called a hypercomputer.) • But the machinery of the computer will probably have to be allowed to do more than compute before it can be made to behave intelligently. As Turing [26] put it, “Intel... |

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Citation Context ...(or Zog-fa’s). A Zog-fa has no inputs and its outputs can be represented by a one-way (to the right) infinite tape that contains only 0’s and 1’s. We will call such a tape an oracle (following Turing =-=[23]-=-). With each such tape we can associate a representing function, f, such that f(n) = 0 if the nth symbol of the tape is 0 and f(n) = 1 if it is a 1. We can then think of a learner that tries to acquir... |

18 |
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Citation Context ...imiting-computable learner can be universal. The idea of a limiting computation is not new. Such a computation was used by Gödel [9] in his proof of the completeness of the predicate calculus. Turing =-=[24]-=- seems to have suggested that something like a limiting computation might be necessary for machine intelligence when he wrote that “There are indications that it is possible to make the (computer) dis... |

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Citation Context ...ious mistakes.” Gold [10] and Putnam [19] showed how this idea could be formalized. The use of limiting computable procedures to do induction has been studied by many, including Burgin [2] and myself =-=[14]-=-. 5. Therefore… I have suggested that machine intelligence (and perhaps the human kind) might involve two separate abilities – the ability to acquire programs and the ability to apply them. I have loo... |

13 |
The Logic of Scientific Discovery (translated from German in
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Citation Context ...dents. And then it might use those theories to try to adapt its behavior to their needs. • Programs that generate theories from evidence 14Predictors with limiting computable learners model Popper’s =-=[18]-=- account of the scientific method and they might, therefore, be used to automate certain kinds of theory generation. Popper argued that, when scientists try to come up with general theories from speci... |

10 | Trial and error predicates and the solution to a problem of - Putnam - 1965 |

5 | Super-recursive algorithms as a tool for high performance computing
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(Show Context)
Citation Context ... game. The computer wins if it can fool the judge for a specified period of time. 1not give rise to random behaviour, or to pointless repetitive loops.” (In other words, it might require what Burgin =-=[3]-=- has called super-recursive algorithms.) • The required “departure” will probably require allowing the computer to make mistakes because, again in Turing’s words [25], “if a machine is expected to be ... |

3 |
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(Show Context)
Citation Context ... occasional serious mistakes.” Gold [10] and Putnam [19] showed how this idea could be formalized. The use of limiting computable procedures to do induction has been studied by many, including Burgin =-=[2]-=- and myself [14]. 5. Therefore… I have suggested that machine intelligence (and perhaps the human kind) might involve two separate abilities – the ability to acquire programs and the ability to apply ... |

3 | Computing machines can’t be intelligent (:::and Turing said so
- Kugel
- 2002
(Show Context)
Citation Context ...tion of “computing machinery”, in terms of what we now call the “Turing machine” [22], he lacked a precise definition of “intelligence”. So, instead of discussing intelligence, he changed the subject =-=[15]-=- and discussed what he called the “imitation game” [26] instead 1 . If we try to use the ability to play the imitation game as a definition of “intelligence” (as some people have done), we quickly not... |

2 |
Die Vollstandikeit der Axiome des logischen Funktionenkalkuls
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(Show Context)
Citation Context ...the set of all Zog-tm’s and partial if it cannot. Theorem 3 says that limiting-computable learner can be universal. The idea of a limiting computation is not new. Such a computation was used by Gödel =-=[9]-=- in his proof of the completeness of the predicate calculus. Turing [24] seems to have suggested that something like a limiting computation might be necessary for machine intelligence when he wrote th... |

2 | Frames of Mind: The Theoryof Multiple Intelligences, Basic Books - Gardner - 1983 |

1 |
How We Know What
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(Show Context)
Citation Context ...sal algorithms we might want to look into types of superrecursive algorithms that are more powerful than limiting-computable ones and that can, therefore, cover the set of all Turing machines. Burgin =-=[4]-=- has called abstract machines that use them “inductive Turing machines of the second order” and I have called them “hyper trial and error” machines [14]. A more general, and more abstract, discussion ... |

1 | Inductive inference: theoryand methods - Angluin, Smith - 1983 |

1 | How we know what technologycan do - Burgin |

1 | Recursive predicates and quanti ers - Kleene - 1943 |

1 | The Structure of Scienti c Revolutions, Universityof - Kuhn - 1962 |

1 | The Logic of Scienti c Discovery, (translation of Logik der Forschung - Popper - 1959 |

1 | Computing machineryand intelligence, Mind 59 (N.S - Turing - 1950 |

1 | Lecture to The London Mathematical Societyon 20 February1947 - Turing - 1986 |