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40
Universal intelligence: A definition of machine intelligence
 Minds and Machines
, 2007
"... A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of ..."
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Cited by 42 (11 self)
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A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.
Incompleteness Theorems for Random Reals
, 1987
"... We obtain some dramatic results using statistical mechanicsthermodynamics kinds of arguments concerning randomness, chaos, unpredictability, and uncertainty in mathematics. We construct an equation involving only whole numbers and addition, multiplication, and exponentiation, with the property tha ..."
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Cited by 32 (1 self)
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We obtain some dramatic results using statistical mechanicsthermodynamics kinds of arguments concerning randomness, chaos, unpredictability, and uncertainty in mathematics. We construct an equation involving only whole numbers and addition, multiplication, and exponentiation, with the property that if one varies a parameter and asks whether the number of solutions is finite or infinite, the answer to this question is indistinguishable from the result of independent tosses of a fair coin. This yields a number of powerful Godel incompletenesstype results concerning the limitations of the axiomatic method, in which entropyinformation measures are used. c fl 1987 Academic Press, Inc. 2 G. J. Chaitin 1. Introduction It is now half a century since Turing published his remarkable paper On Computable Numbers, with an Application to the Entscheidungsproblem (Turing [15]). In that paper Turing constructs a universal Turing machine that can simulate any other Turing machine. He also use...
A Formal Definition of Intelligence Based on an Intensional Variant of Algorithmic Complexity
 In Proceedings of the International Symposium of Engineering of Intelligent Systems (EIS'98
, 1998
"... Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like lcalculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] ..."
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Cited by 30 (17 self)
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Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like lcalculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] with two remarkable features inherited from its objectoriented coding in C++: it is easily tunable for our needs, and it is efficient. We have made it even more reduced, removing any operand in the instruction set, even for the loop operations. We have only three registers which are AX (the accumulator), BX and CX. The operations Q b we have used for our experiment are in Table 1: LOOPTOP Decrements CX. If it is not equal to the first element jump to the program top.
From Heisenberg to Gödel via Chaitin
 INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
, 2004
"... In 1927 Heisenberg discovered that the "more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa". Four years later ..."
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Cited by 11 (9 self)
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In 1927 Heisenberg discovered that the "more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa". Four years later
Algorithmic Information & Evolution
, 1991
"... A theory of information and computation has been developed: "algorithmic information theory." Two books [1112] have recently been published on this subject, as well as a number of nontechnical discussions [1316]. The main thrust of algorithmic information theory is twofold: (1) an informationth ..."
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Cited by 10 (1 self)
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A theory of information and computation has been developed: "algorithmic information theory." Two books [1112] have recently been published on this subject, as well as a number of nontechnical discussions [1316]. The main thrust of algorithmic information theory is twofold: (1) an informationtheoretic mathematical definition of random sequence via algorithmic incompressibility, and (2) strong informationtheoretic versions of Godel's incompleteness theorem. The 1 halting probability# of a universal Turing machine plays a fundamental role.# is an abstract example of evolution: it is of infinite complexity and the limit of a computable sequence of rational numbers.
ON INTERPRETING CHAITIN’S INCOMPLETENESS THEOREM
, 1998
"... The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin’s famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number ..."
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Cited by 9 (0 self)
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The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin’s famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of the strength of the theory. I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental.
Is Complexity a Source of Incompleteness?
 IS COMPLEXITY A SOURCE OF INCOMPLETENESS
, 2004
"... ..."
Informationtheoretic Incompleteness
 APPLIED MATHEMATICS AND COMPUTATION
, 1992
"... We propose an improved definition of the complexity of a formal axiomatic system: this is now taken to be the minimum size of a selfdelimiting program for enumerating the set of theorems of the formal system. Using this new definition, we show (a) that no formal system of complexity n can exhibit a ..."
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Cited by 7 (1 self)
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We propose an improved definition of the complexity of a formal axiomatic system: this is now taken to be the minimum size of a selfdelimiting program for enumerating the set of theorems of the formal system. Using this new definition, we show (a) that no formal system of complexity n can exhibit a specific object with complexity greater than n + c, and (b) that a formal system of complexity n can determine at most n + c scattered bits of the halting probability\Omega . We also present a short, selfcontained proof of (b).