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A Theory for Mentally Developing Robots
"... This paper introduces a theory about mentally developing robots. The limitation of the traditional agent model is raised and a new SASE agent is proposed, based on our SAIL developmental robot. We formulate the manual development paradigm and autonomous development paradigm. The performance of a dev ..."
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Cited by 22 (5 self)
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This paper introduces a theory about mentally developing robots. The limitation of the traditional agent model is raised and a new SASE agent is proposed, based on our SAIL developmental robot. We formulate the manual development paradigm and autonomous development paradigm. The performance of a developmental robot is then formulated as reaching the norm of a human age group. The framework of autonomously generating brain 1 representation is investigated in mathematical terms. Some techniques of such a representation are provided based on our SAIL2 developmental algorithm. We establish the conceptual limitation of symbolic representation and from the limitation we propose that no developmental robot can use a symbolic representation. Finally, the completeness of developmental robot is investigated conditioned on five factors.
Ultimate Cognition à la Gödel
 COGN COMPUT
, 2009
"... "All life is problem solving," said Popper. To deal with arbitrary problems in arbitrary environments, an ultimate cognitive agent should use its limited hardware in the "best" and "most efficient" possible way. Can we formally nail down this informal statement, and der ..."
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Cited by 20 (11 self)
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"All life is problem solving," said Popper. To deal with arbitrary problems in arbitrary environments, an ultimate cognitive agent should use its limited hardware in the "best" and "most efficient" possible way. Can we formally nail down this informal statement, and derive a mathematically rigorous blueprint of ultimate cognition? Yes, we can, using Kurt Gödel’s celebrated selfreference trick of 1931 in a new way. Gödel exhibited the limits of mathematics and computation by creating a formula that speaks about itself, claiming to be unprovable by an algorithmic theorem prover: either the formula is true but unprovable, or math itself is flawed in an algorithmic sense. Here we describe an agentcontrolling program that speaks about itself, ready to rewrite itself in arbitrary fashion once it has found a proof that the rewrite is useful according to a userdefined utility function. Any such a rewrite is necessarily globally optimal—no local maxima!—since this proof necessarily must have demonstrated the uselessness of continuing the proof search for even better rewrites. Our selfreferential program will optimally speed up its proof searcher and other program parts, but only if the speed up’s utility is indeed provable—even ultimate cognition has limits of the Gödelian kind.
From Total Equational to Partial First Order Logic
, 1998
"... The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to pa ..."
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Cited by 19 (8 self)
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The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to partiality, like (variants of) error algebras and ordersortedness are also discussed, showing their uses and limitations. Moreover, both the total and the partial (positive) conditional fragment are investigated in detail, and in particular the existence of initial (free) models for such restricted logical paradigms is proved. Some more powerful algebraic frameworks are sketched at the end. Equational specifications introduced in last chapter, are a powerful tool to represent the most common data types used in programming languages and their semantics. Indeed, Bergstra and Tucker have shown in a series of papers (see [BT87] for a complete exposition of results) that a data type is semicompu...
Is Independence an Exception?
, 1994
"... Gödel's Incompleteness Theorem asserts that any sufficiently rich, sound, and recursively axiomatizable theory is incomplete. We show that, in a quite general topological sense, incompleteness is a rather common phenomenon: With respect to any reasonable topology the set of true and unprovable ..."
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Cited by 18 (12 self)
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Gödel's Incompleteness Theorem asserts that any sufficiently rich, sound, and recursively axiomatizable theory is incomplete. We show that, in a quite general topological sense, incompleteness is a rather common phenomenon: With respect to any reasonable topology the set of true and unprovable statements of such a theory is dense and in many cases even corare.
Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes
, 2009
"... I argue that data becomes temporarily interesting by itself to some selfimproving, but computationally limited, subjective observer once he learns to predict or compress the data in a better way, thus making it subjectively simpler and more beautiful. Curiosity is the desire to create or discover m ..."
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Cited by 18 (7 self)
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I argue that data becomes temporarily interesting by itself to some selfimproving, but computationally limited, subjective observer once he learns to predict or compress the data in a better way, thus making it subjectively simpler and more beautiful. Curiosity is the desire to create or discover more nonrandom, nonarbitrary, regular data that is novel and surprising not in the traditional sense of Boltzmann and Shannon but in the sense that it allows for compression progress because its regularity was not yet known. This drive maximizes interestingness, the first derivative of subjective beauty or compressibility, that is, the steepness of the learning curve. It motivates exploring infants, pure mathematicians, composers,
Metaprogramming in Logic
 ENCYCLOPEDIA OF COMPUTER SCIENCE AND TECHNOLOGY
, 1994
"... In this review of metaprogramming in logic we pay equal attention to theoretical and practical issues: the contents range from mathematical and logical preliminaries to implementation and applications in, e.g., software engineering and knowledge representation. The area is one in rapid development b ..."
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Cited by 17 (0 self)
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In this review of metaprogramming in logic we pay equal attention to theoretical and practical issues: the contents range from mathematical and logical preliminaries to implementation and applications in, e.g., software engineering and knowledge representation. The area is one in rapid development but we have emphasized such issues that are likely to be important for future metaprogramming languages and methodologies.
The New AI: General & Sound & Relevant for Physics
 ARTIFICIAL GENERAL INTELLIGENCE (ACCEPTED 2002)
, 2003
"... Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, induct ..."
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Cited by 16 (9 self)
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Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inductive inference based on Occam’s razor, problem solving, decision making, and reinforcement learning in environments of a very general type. Since inductive inference is at the heart of all inductive sciences, some of the results are relevant not only for AI and computer science but also for physics, provoking nontraditional predictions based on Zuse’s thesis of the computergenerated universe.
Gödel Machines: SelfReferential Universal Problem Solvers Making Provably Optimal SelfImprovements
, 2003
"... An old dream of computer scientists is to build an optimally efficient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Gödel's celebrated selfreferential formulas (1931). Our Gödel machine's initial software includes ..."
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Cited by 16 (7 self)
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An old dream of computer scientists is to build an optimally efficient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Gödel's celebrated selfreferential formulas (1931). Our Gödel machine's initial software includes an axiomatic description of: the Gödel machine's hardware, the problemspecific utility function (such as the expected future reward of a robot), known aspects of the environment, costs of actions and computations, and the initial software itself (this is possible without introducing circularity). It also includes a typically suboptimal initial problemsolving policy and an asymptotically optimal proof searcher searching the space of computable proof techniques  that is, programs whose outputs are proofs. Unlike previous approaches, the selfreferential Gödel machine will rewrite any part of its software, including axioms and proof searcher, as soon as it has found a proof that this will improve its future performance, given its typically limited computational resources. We show that selfrewrites are globally optimal  no local minima!since provably none of all the alternative rewrites and proofs (those that could be found by continuing the proof search) are worth waiting for.
HigherOrder Tableaux
, 1995
"... Even though higherorder calculi for automated theorem proving are rather old, tableau calculi have not been investigated yet. This paper presents two free variable tableau calculi for higherorder logic that use higherorder unification as the key inference procedure. These calculi differ in the ..."
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Cited by 16 (6 self)
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Even though higherorder calculi for automated theorem proving are rather old, tableau calculi have not been investigated yet. This paper presents two free variable tableau calculi for higherorder logic that use higherorder unification as the key inference procedure. These calculi differ in the treatment of the substitutional properties of equivalences. The first calculus is equivalent in deductive power to the machineoriented higherorder refutation calculi known from the literature, whereas the second is complete with respect to Henkin's general models.
Computation and Hypercomputation
 MINDS AND MACHINES
, 2003
"... Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computationality in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification o ..."
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Cited by 15 (4 self)
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Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computationality in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because noncomputable values are indistinguishable from sufficiently close computable approximations. In addition to