TY - GEN

T1 - Abstraction super-structuring normal forms

T2 - Ray Solomonoff 85th Memorial Conference on Algorithmic Probability and Friends: Bayesian Prediction and Artificial Intelligence

AU - Silvescu, Adrian

AU - Honavar, Vasant

PY - 2013

Y1 - 2013

N2 - Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minimalistic set of operations on structural elements in terms of which any theory can be expressed. We identify abstraction (grouping similar entities) and super-structuring (combining topologically e.g., spatio-temporally close entities) as the essential structural operations in the induction process. We show that only two more structural operations, namely, reverse abstraction and reverse super-structuring (the duals of abstraction and super-structuring respectively) suffice in order to exploit the full power of Turing-equivalent generative grammars in induction. We explore the implications of this theorem with respect to the nature of hidden variables, radical positivism and the 2-century old claim of David Hume about the principles of connexion among ideas.

AB - Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minimalistic set of operations on structural elements in terms of which any theory can be expressed. We identify abstraction (grouping similar entities) and super-structuring (combining topologically e.g., spatio-temporally close entities) as the essential structural operations in the induction process. We show that only two more structural operations, namely, reverse abstraction and reverse super-structuring (the duals of abstraction and super-structuring respectively) suffice in order to exploit the full power of Turing-equivalent generative grammars in induction. We explore the implications of this theorem with respect to the nature of hidden variables, radical positivism and the 2-century old claim of David Hume about the principles of connexion among ideas.

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U2 - 10.1007/978-3-642-44958-1_27

DO - 10.1007/978-3-642-44958-1_27

M3 - Conference contribution

AN - SCOPUS:84893206552

SN - 9783642449574

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 339

EP - 350

BT - Algorithmic Probability and Friends

PB - Springer Verlag

Y2 - 30 November 2011 through 2 December 2011

ER -