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A neural network structure specified for representing and storing logical relations

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Abstract

Logical representation and reasoning is an important aspect of intelligence. Current ANN models are good at perceptual intelligence while they are not good at cognitive intelligence such as logical representation, so researchers have tried to design novel models so as to represent and store logical relations into the neural network structures, called the type of Knowledge-Based Neural Network. However, there is an ambiguous problem that the same neural network structure represents multiple logical relations. It causes the corresponding logical relations not to be read out from these neural network structures which are constructed according to them. To let logical relations stored in the format of neural network and read out from it, this paper studies the direct mapping method between logical relations and neural network structures and proposes a novel model called Probabilistic Logical Generative Neural Network, which is specified for logical relation representation by redesigning the neurons and links. It can make neurons solely for representing things while making links solely for representing logical relations between things, and thus no extra logical neurons and layers are needed. Moreover, the related construction and adjustment methods of the neural network structure are also designed making the neural network structure dynamically constructed and adjusted according to logical relations.

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Acknowledgements

This work was funded by the NSFC (National Natural Science Foundation of China) Grant No. 61503273.

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Authors and Affiliations

  1. Department of Computer Science and Technology, Taiyuan University of Technology, Taiyuan, China

    Gang Wang

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  1. Gang Wang
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Correspondence to Gang Wang.

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Appendices

Appendix 1: Supplements

In the following, it is a simple rule library as example which has 14 logical relations. The PLGNN in Fig. 11 memorizes and stores them through the interconnection structure of the neural network.

  1. 1.

    If an animal has hair, then it is mammal.

  2. 2.

    If an animal produces milk, then it is mammal.

  3. 3.

    If a mammal is predator, then it is beast.

  4. 4.

    If a mammal has hoof, then it is ungulate.

  5. 5.

    If a mammal is ruminant, then it is ungulate.

  6. 6.

    If an animal has feather, produces egg, then it is bird.

  7. 7.

    If an animal airborne, then it is bird.

  8. 8.

    If a beast is yellow and spots, then it is leopard.

  9. 9.

    If a beast is yellow and black strips, then it is tiger.

  10. 10.

    If an ungulate has long neck, long leg, yellow and spots, then it is giraffe.

  11. 11.

    If an ungulate is white and black strips, then it is zebra.

  12. 12.

    If a bird cannot airborne, has long neck, long legs, and is mixture of black and white, then it is ostrich.

  13. 13.

    If a bird cannot airborne, can aquatic, and is mixture of black and white, then it is penguin.

  14. 14.

    If a bird can airborne, then it is swallow.

These relations often appeared as example and appeared in AI-related papers and books such as Neural Networks and Learning Machines written by Haykin.

Appendix 2

The algorithms of the construction and adjustment of the neural network structure are shown in Fig. 12.

Fig. 12
figure 12

Algorithms of construction and adjustment of neural network structure

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Wang, G. A neural network structure specified for representing and storing logical relations. Neural Comput & Applic 32, 14975–14993 (2020). https://doi.org/10.1007/s00521-020-04852-4

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