Solving tree problems with category theory

Rafik Hadfi

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

Artificial Intelligence (AI) has long pursued models, theories, and techniques to imbue machines with human-like general intelligence. Yet even the currently predominant data-driven approasches in AI seem to be lacking humans’ unique ability to solve wide ranges of problems. This situation begs the question of the existence of principles that underlie general problem-solving capabilities. We approach this question through the mathematical formulation of analogies across different problems and solutions. We focus in particular on problems that could be represented as tree-like structures. Most importantly, we adopt a category-theoretic approach in formalising tree problems as categories, and in proving the existence of equivalences across apparently unrelated problem domains. We prove the existence of a functor between the category of tree problems and the category of solutions. We also provide a weaker version of the functor by quantifying equivalences of problem categories using a metric on tree problems.

Original languageEnglish
Title of host publicationArtificial General Intelligence
Subtitle of host publication11th International Conference, AGI 2018, Proceedings
EditorsMatthew Ikle, Arthur Franz, Rafal Rzepka, Ben Goertzel
Place of PublicationSwitzerland
PublisherSpringer
Pages62-76
Number of pages15
ISBN (Electronic)9783319976761
ISBN (Print)9783319976754
DOIs
Publication statusPublished - 1 Jan 2018
EventConference on Artificial General Intelligence (AGI) 2018 - Prague, Czech Republic
Duration: 22 Aug 201825 Aug 2018
Conference number: 11th

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10999 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceConference on Artificial General Intelligence (AGI) 2018
Abbreviated titleAGI 2018
CountryCzech Republic
CityPrague
Period22/08/1825/08/18

Keywords

  • Analogy-making
  • Artificial general intelligence
  • Category theory
  • Decision tree
  • Functor
  • Maze problem
  • Problem solving
  • Transfer learning

Cite this

Hadfi, R. (2018). Solving tree problems with category theory. In M. Ikle, A. Franz, R. Rzepka, & B. Goertzel (Eds.), Artificial General Intelligence: 11th International Conference, AGI 2018, Proceedings (pp. 62-76). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10999 LNAI). Switzerland: Springer. https://doi.org/10.1007/978-3-319-97676-1_7
Hadfi, Rafik. / Solving tree problems with category theory. Artificial General Intelligence: 11th International Conference, AGI 2018, Proceedings. editor / Matthew Ikle ; Arthur Franz ; Rafal Rzepka ; Ben Goertzel. Switzerland : Springer, 2018. pp. 62-76 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Hadfi, R 2018, Solving tree problems with category theory. in M Ikle, A Franz, R Rzepka & B Goertzel (eds), Artificial General Intelligence: 11th International Conference, AGI 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10999 LNAI, Springer, Switzerland, pp. 62-76, Conference on Artificial General Intelligence (AGI) 2018, Prague, Czech Republic, 22/08/18. https://doi.org/10.1007/978-3-319-97676-1_7

Solving tree problems with category theory. / Hadfi, Rafik.

Artificial General Intelligence: 11th International Conference, AGI 2018, Proceedings. ed. / Matthew Ikle; Arthur Franz; Rafal Rzepka; Ben Goertzel. Switzerland : Springer, 2018. p. 62-76 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10999 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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Hadfi R. Solving tree problems with category theory. In Ikle M, Franz A, Rzepka R, Goertzel B, editors, Artificial General Intelligence: 11th International Conference, AGI 2018, Proceedings. Switzerland: Springer. 2018. p. 62-76. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-97676-1_7