### 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 language | English |
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Title of host publication | Artificial General Intelligence |

Subtitle of host publication | 11th International Conference, AGI 2018, Proceedings |

Editors | Matthew Ikle, Arthur Franz, Rafal Rzepka, Ben Goertzel |

Place of Publication | Switzerland |

Publisher | Springer |

Pages | 62-76 |

Number of pages | 15 |

ISBN (Electronic) | 9783319976761 |

ISBN (Print) | 9783319976754 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

Event | Conference on Artificial General Intelligence (AGI) 2018 - Prague, Czech Republic Duration: 22 Aug 2018 → 25 Aug 2018 Conference number: 11th |

### Publication series

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

Volume | 10999 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | Conference on Artificial General Intelligence (AGI) 2018 |
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Abbreviated title | AGI 2018 |

Country | Czech Republic |

City | Prague |

Period | 22/08/18 → 25/08/18 |

### Keywords

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

### Cite this

*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

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - Solving tree problems with category theory

AU - Hadfi, Rafik

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Analogy-making

KW - Artificial general intelligence

KW - Category theory

KW - Decision tree

KW - Functor

KW - Maze problem

KW - Problem solving

KW - Transfer learning

UR - http://www.scopus.com/inward/record.url?scp=85051437737&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-97676-1_7

DO - 10.1007/978-3-319-97676-1_7

M3 - Conference Paper

SN - 9783319976754

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

SP - 62

EP - 76

BT - Artificial General Intelligence

A2 - Ikle, Matthew

A2 - Franz, Arthur

A2 - Rzepka, Rafal

A2 - Goertzel, Ben

PB - Springer

CY - Switzerland

ER -