Abstraction super-structuring normal forms: Towards a theory of structural induction

Adrian Silvescu, Vasant Honavar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationAlgorithmic Probability and Friends: Bayesian Prediction and Artificial Intelligence - Papers from the Ray Solomonoff 85th Memorial Conference
Pages339-350
Number of pages12
Volume7070 LNAI
DOIs
StatePublished - 2013
EventRay Solomonoff 85th Memorial Conference on Algorithmic Probability and Friends: Bayesian Prediction and Artificial Intelligence - Melbourne, VIC, Australia
Duration: Nov 30 2011Dec 2 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7070 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

OtherRay Solomonoff 85th Memorial Conference on Algorithmic Probability and Friends: Bayesian Prediction and Artificial Intelligence
CountryAustralia
CityMelbourne, VIC
Period11/30/1112/2/11

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Theoretical Computer Science

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    Silvescu, A., & Honavar, V. (2013). Abstraction super-structuring normal forms: Towards a theory of structural induction. In Algorithmic Probability and Friends: Bayesian Prediction and Artificial Intelligence - Papers from the Ray Solomonoff 85th Memorial Conference (Vol. 7070 LNAI, pp. 339-350). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7070 LNAI). https://doi.org/10.1007/978-3-642-44958-1-27