### Abstract

The universal differential and difference equation form an important basis for reified temporal-causal networks and their implementation. In this chapter, a more in depth analysis is presented of the universal differential and difference equation. It is shown how these equations can be derived in a direct manner and they are illustrated by some examples. Due to the existence of these universal difference and differential equation, the class of temporal-causal networks is closed under reification: by them it can be guaranteed that any reification of a temporal-causal network is itself also a temporal-causal network. That means that dedicated modeling and analysis methods for temporal-causal networks can also be applied to reified temporal-causal networks. In particular, it guarantees that reification can be done iteratively in order to obtain multilevel reified network models that are very useful to model multiple orders of adaptation. Moreover, as shown in Chap. 9, the universal difference equation enables that software of a very compact form can be developed, as all reification levels are handled by one computational reified network engine in the same manner. Alternatively, it is shown how the universal difference or differential equation can be used for compilation by multiple substitution for all states, which leads to another form of implementation. The background of these issues is discussed in the current chapter.

Original language | English |
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Title of host publication | Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models |

Editors | Jan Treur |

Publisher | Springer International Publishing AG |

Chapter | 10 |

Pages | 225-247 |

Number of pages | 23 |

DOIs | |

Publication status | Published - 1 Jan 2020 |

### Publication series

Name | Studies in Systems, Decision and Control |
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Volume | 251 |

ISSN (Print) | 2198-4182 |

ISSN (Electronic) | 2198-4190 |

### Fingerprint

### Cite this

*Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models*(pp. 225-247). (Studies in Systems, Decision and Control; Vol. 251). Springer International Publishing AG. https://doi.org/10.1007/978-3-030-31445-3_10

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*Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models.*Studies in Systems, Decision and Control, vol. 251, Springer International Publishing AG, pp. 225-247. https://doi.org/10.1007/978-3-030-31445-3_10

**On the universal combination function and the universal difference equation for reified temporal-causal network models.** / Treur, Jan.

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

TY - CHAP

T1 - On the universal combination function and the universal difference equation for reified temporal-causal network models

AU - Treur, Jan

PY - 2020/1/1

Y1 - 2020/1/1

N2 - The universal differential and difference equation form an important basis for reified temporal-causal networks and their implementation. In this chapter, a more in depth analysis is presented of the universal differential and difference equation. It is shown how these equations can be derived in a direct manner and they are illustrated by some examples. Due to the existence of these universal difference and differential equation, the class of temporal-causal networks is closed under reification: by them it can be guaranteed that any reification of a temporal-causal network is itself also a temporal-causal network. That means that dedicated modeling and analysis methods for temporal-causal networks can also be applied to reified temporal-causal networks. In particular, it guarantees that reification can be done iteratively in order to obtain multilevel reified network models that are very useful to model multiple orders of adaptation. Moreover, as shown in Chap. 9, the universal difference equation enables that software of a very compact form can be developed, as all reification levels are handled by one computational reified network engine in the same manner. Alternatively, it is shown how the universal difference or differential equation can be used for compilation by multiple substitution for all states, which leads to another form of implementation. The background of these issues is discussed in the current chapter.

AB - The universal differential and difference equation form an important basis for reified temporal-causal networks and their implementation. In this chapter, a more in depth analysis is presented of the universal differential and difference equation. It is shown how these equations can be derived in a direct manner and they are illustrated by some examples. Due to the existence of these universal difference and differential equation, the class of temporal-causal networks is closed under reification: by them it can be guaranteed that any reification of a temporal-causal network is itself also a temporal-causal network. That means that dedicated modeling and analysis methods for temporal-causal networks can also be applied to reified temporal-causal networks. In particular, it guarantees that reification can be done iteratively in order to obtain multilevel reified network models that are very useful to model multiple orders of adaptation. Moreover, as shown in Chap. 9, the universal difference equation enables that software of a very compact form can be developed, as all reification levels are handled by one computational reified network engine in the same manner. Alternatively, it is shown how the universal difference or differential equation can be used for compilation by multiple substitution for all states, which leads to another form of implementation. The background of these issues is discussed in the current chapter.

UR - http://www.scopus.com/inward/record.url?scp=85075174616&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075174616&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-31445-3_10

DO - 10.1007/978-3-030-31445-3_10

M3 - Chapter

T3 - Studies in Systems, Decision and Control

SP - 225

EP - 247

BT - Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models

A2 - Treur, Jan

PB - Springer International Publishing AG

ER -