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Is there an Elegant Universal Theory of Prediction?
 IDSIA / USISUPSI DALLE MOLLE INSTITUTE FOR ARTIFICIAL INTELLIGENCE. GALLERIA 2, 6928
, 2006
"... Solomonoff’s inductive learning model is a powerful, universal and highly elegant theory of sequence prediction. Its critical flaw is that it is incomputable and thus cannot be used in practice. It is sometimes suggested that it may still be useful to help guide the development of very general and p ..."
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Solomonoff’s inductive learning model is a powerful, universal and highly elegant theory of sequence prediction. Its critical flaw is that it is incomputable and thus cannot be used in practice. It is sometimes suggested that it may still be useful to help guide the development of very general and powerful theories of prediction which are computable. In this paper it is shown that although powerful algorithms exist, they are necessarily highly complex. This alone makes their theoretical analysis problematic, however it is further shown that beyond a moderate level of complexity the analysis runs into the deeper problem of Gödel incompleteness. This limits the power of mathematics to analyse and study prediction algorithms, and indeed intelligent systems in general.
Open problems in universal induction & intelligence
 Algorithms
, 2009
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Measuring Cognitive Abilities of Machines, Humans and NonHuman Animals in a Unified Way: towards Universal Psychometrics
, 2012
"... We present and develop the notion of ‘universal psychometrics’ as a subject of study, and eventually a discipline, that focusses on the measurement of cognitive abilities for the machine kingdom, which comprises any kind of individual or collective, either artificial, biological or hybrid. Universal ..."
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We present and develop the notion of ‘universal psychometrics’ as a subject of study, and eventually a discipline, that focusses on the measurement of cognitive abilities for the machine kingdom, which comprises any kind of individual or collective, either artificial, biological or hybrid. Universal psychometrics can be built, of course, upon the experience, techniques and methodologies from (human) psychometrics, comparative cognition and related areas. Conversely, the perspective and techniques which are being developed in the area of machine intelligence measurement using (algorithmic) information theory can be of much broader applicability and implication outside artificial intelligence. This general approach to universal psychometrics spurs the reunderstanding of most (if not all) of the big issues about the measurement of cognitive abilities, and creates a new foundation for (re)defining and mathematically formalising the concept of cognitive task, evaluable subject, interface, task choice, difficulty, agent response curves, etc. We introduce the notion of a universal cognitive test and discuss whether (and when) it may be necessary for exploring the machine kingdom. On the issue of intelligence and very general abilities, we also get some results and connections with the related notions of nofreelunch theorems and universal priors.
Turing Machines and Recursive Turing Tests
"... Abstract. The Turing Test, in its standard interpretation, has been dismissed by many as a practical intelligence test. In fact, it is questionable that the imitation game was meant by Turing himself to be used as a test for evaluating machines and measuring the progress of artificial intelligence. ..."
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Abstract. The Turing Test, in its standard interpretation, has been dismissed by many as a practical intelligence test. In fact, it is questionable that the imitation game was meant by Turing himself to be used as a test for evaluating machines and measuring the progress of artificial intelligence. In the past fifteen years or so, an alternative approach to measuring machine intelligence has been consolidating. The key concept for this alternative approach is not the Turing Test, but the Turing machine, and some theories derived upon it, such as Solomonoff’s theory of prediction, the MML principle, Kolmogorov complexity and algorithmic information theory. This presents an antagonistic view to the Turing test, where intelligence tests are based on formal principles, are not anthropocentric, are meaningful computationally and the abilities (or factors) which are evaluated can be recognised and quantified. Recently, however, this computational view has been touching upon issues which are somewhat related to the Turing Test, namely that we may need other intelligent agents in the tests. Motivated by these issues (and others), this paper links these two antagonistic views by bringing some of the ideas around the Turing Test to the realm of Turing machines.
Algorithmically Independent Sequences
, 2008
"... Two objects are independent if they do not affect each other. Independence is wellunderstood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper proposes two types of independence for arbitrary infinite bi ..."
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Two objects are independent if they do not affect each other. Independence is wellunderstood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper proposes two types of independence for arbitrary infinite binary sequences and studies their properties. Our two proposed notions of independence have some of the intuitive properties that one naturally expects. For example, for every sequence x, the set of sequences that are independent (in the weaker of the two senses) with x has measure one. For both notions of independence we investigate to what extent pairs of independent sequences, can be effectively constructed via Turing reductions (from one or more input sequences). In this respect, we prove several impossibility results. For example, it is shown that there is no effective way of producing from an arbitrary sequence with positive constructive Hausdorff dimension two sequences that are independent (even in the weaker type of independence) and have superlogarithmic complexity. Finally, a few conjectures and open questions are discussed.
Characterizing the Software Development Process: A New Approach Based on Kolmogorov Complexity
 in Computer Aided Systems Theory  EUROCAST’2001, 8th International Workshop on Computer Aided Systems Theory, ser. Lecture Notes in Computer Science
, 2001
"... Our main aim is to propose a new characterization for the software development process. We suggest that software development methodology has some limits. These limits are a clue that software development process is more subjective and empirical than objective and formal. We use Kolmogorov complexity ..."
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Our main aim is to propose a new characterization for the software development process. We suggest that software development methodology has some limits. These limits are a clue that software development process is more subjective and empirical than objective and formal. We use Kolmogorov complexity to develop the formal argument and to outline the informal conclusions. Kolmogorov complexity is based on the size in bits of the smallest e ective description of an object and is a suitable quantitative measure of the object's information content.
Gödel incompleteness revisited
 Proceedings of the First Symposium on Cellular Automata Journées Automates Cellulaires (JAC’2008
, 2008
"... Abstract. We investigate the frontline of Gödel’s incompleteness theorems ’ proofs and the links with computability. The Gödel incompleteness phenomenon Gödel’s incompleteness theorems [Göd31, SFKM+86] are milestones in the subject of mathematical logic. Apart from Gödel’s original syntactical ..."
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Abstract. We investigate the frontline of Gödel’s incompleteness theorems ’ proofs and the links with computability. The Gödel incompleteness phenomenon Gödel’s incompleteness theorems [Göd31, SFKM+86] are milestones in the subject of mathematical logic. Apart from Gödel’s original syntactical proof, many other proofs have been presented. Kreisel’s proof [Kre68] was the first with a modeltheoretical flavor. Most of these proofs are attempts to get rid of any form of selfreferential reasoning, even if there remains diagonalization arguments in each of these proofs. The reason for this quest holds in the fact that the diagonalization lemma, when used as a method of constructing an independent statement, is intuitively unclear. Boolos ’ proof [Boo89b] was the first attempt in this direction and gave rise to many other attempts. Sometimes, it unfortunately sounds a bit like finding a way to sweep selfreference under the mathematical rug. One of these attempts has been to prove the incompleteness theorems using another paradox than the Richard and the Liar paradoxes. It is interesting to note that, in his
Emergence: an algorithmic formulation
, 2005
"... When the microequations of a dynamical system generate complex macrobehaviour, there can be an explanatory gap between the smallscale and largescale descriptions of the same system. The microdynamics may be simple, but its relationship to the macrobehaviour may seem impenetrable. This phenomenon, ..."
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When the microequations of a dynamical system generate complex macrobehaviour, there can be an explanatory gap between the smallscale and largescale descriptions of the same system. The microdynamics may be simple, but its relationship to the macrobehaviour may seem impenetrable. This phenomenon, known as emergence, poses problems for the nature of scientific understanding. How do we reconcile two radically different modes of description? Emergence is formulated using the powerful tools of algorithmic information and computational theory. This provides the ground for an extension and generalisation of the phenomenon. Mathematics itself is analysed as an emergent system, linking formalist notions of mathematics as a string manipulation game with the more abstract ideas and proofs that occupy mathematicians. A philosophical problem that has plagued emergence is whether the whole can be more than the sum of its parts. This possibility, known as strong emergence, manifests when emergent macrostructures introduce brand new causal dynamics into a system. A new perspective on this