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58
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 63 (17 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 43 (0 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 & H ..."
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Cited by 38 (19 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.
Compression and intelligence: social environments and communication
"... Abstract. Compression has been advocated as one of the principles which pervades inductive inference and prediction and, from there, it has also been recurrent in definitions and tests of intelligence. However, this connection is less explicit in new approaches to intelligence. In this paper, we ad ..."
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Cited by 13 (7 self)
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Abstract. Compression has been advocated as one of the principles which pervades inductive inference and prediction and, from there, it has also been recurrent in definitions and tests of intelligence. However, this connection is less explicit in new approaches to intelligence. In this paper, we advocate that the notion of compression can appear again in definitions and tests of intelligence through the concepts of ‘mindreading’ and ‘communication ’ in the context of multiagent systems and social environments. Our main position is that twopart Minimum Message Length (MML) compression is not only more natural and effective for agents with limited resources, but it is also much more appropriate for agents in (cooperative) social environments than onepart compression schemes particularly those using a posteriorweighted mixture of all available models following Solomonoff’s theory of prediction. We think that the realisation of these differences is important to avoid a naive view of ‘intelligence as compression ’ in favour of a better understanding of how, why and where (onepart or twopart, lossless or lossy) compression is needed.
Is Complexity a Source of Incompleteness?
 IS COMPLEXITY A SOURCE OF INCOMPLETENESS
, 2004
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From Heisenberg to Gödel via Chaitin
, 2008
"... 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 Gödel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. A ..."
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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 Gödel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. As both results express some kind of impossibility it is natural to ask whether there is any relation between them, and, indeed, this question has been repeatedly asked for a long time. The main interest seems to have been in possible implications of incompleteness to physics. In this note we will take interest in the converse implication and will offer a positive answer to the question: Does uncertainty imply incompleteness? We will show that algorithmic randomness is equivalent to a “formal uncertainty principle ” which implies Chaitin’s informationtheoretic incompleteness. We also show that the derived uncertainty relation, for many computers, is physical. This fact supports the conjecture that uncertainty implies randomness not only in mathematics, but also in physics.
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 11 (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.
Algorithmic information and evolution
 in O.Solbrig and G.Nicolis, eds, ‘Perspectives on Biological Complexity’, IUBS
, 1988
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Turing Tests with Turing Machines
"... Comparative tests work by finding the difference (or the absence of difference) between a reference subject and an evaluee. The Turing Test, in its standard interpretation, takes (a subset of) the human species as a reference. Motivated by recent findings and developments in the area of machine inte ..."
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Cited by 8 (5 self)
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Comparative tests work by finding the difference (or the absence of difference) between a reference subject and an evaluee. The Turing Test, in its standard interpretation, takes (a subset of) the human species as a reference. Motivated by recent findings and developments in the area of machine intelligence evaluation, we discuss what it would be like to have a Turing Test where the reference and the interrogator subjects are replaced by Turing Machines. This question sets the focus on several issues that are usually disregarded when dealing with the Turing Test, such as the degree of intelligence of reference and interrogator, the role of imitation (and not only prediction) in intelligence, its view from the perspective of game theory and others. Around these issues, this paper finally brings the Turing Test to the realm of Turing machines.