Approximate Reasoning for Large-Scale ABox in OWL DL Based on Neural-Symbolic Learning
Abstract
:1. Introduction
2. Related Work
2.1. ABox Reasoning Based on Logical Deduction
2.2. ABox Reasoning by KGC
2.3. ABox Reasoning Based on Neural-Symbolic Learning
3. Construction Method of the CFR
3.1. Basic Idea of the CFR
3.2. Framework of the CFR
3.3. Process of the CFR
3.3.1. ABox Synthesis Method
- The first stage is to obtain a set of class assertions by generating instances of each class and then reason over the set of class assertions. First, a given number of instances are generated according to the class in TBox to obtain a set of class assertions. Then, the ontology reasoner named Pellet is employed to perform a logical reasoning on the set of class assertions based on the TBox. The -A relation between the instance and the class is generalized to obtain the -A relation between the instance and the parent or parent-of-parent class and thus obtain the set of reasoned class assertions;
- The second stage is to generate the set of role assertions. According to the relation definition and class constraints, as well as the set of reasoned class assertions, the relation between instances is randomly established. The union of the set of class assertions and the set of relation assertions is the synthesized ABox with noise;
- The third stage is to remove conflict sets from the synthesized ABox with noise to obtain a logically consistent ABox. A set of relation assertions that randomly built may conflict with the set of axioms of the TBox. Based on the minimal conflict set discovery method, all the minimal conflict sets can be obtained from the synthesized ABox with noise and eliminated, and finally, a synthesized ABox with consistent logical expression is obtained.
Algorithm 1: The ABox synthesis method based on TBox |
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3.3.2. Subgraph Segmentation and Dataset Construction
Algorithm 2: Subgraph segmentation and dataset construction |
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3.3.3. Encoding and Decoding Methods
Algorithm 3: The of a multi-layer adjacency matrix |
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Algorithm 4: The of a multi-layer adjacency matrix |
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3.3.4. Structure of the FCNN
3.4. Evaluation Criterions of the CFR
4. Experiments
4.1. Experimental Data and Parameter Settings
4.2. Reasoning Quality of the CFR
4.3. Reasoning Efficiency of the CFR
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Ontology | # Axioms | # Class | # Role | Complexity |
---|---|---|---|---|
Famiy | 153 | 18 | 16 | |
Time | 82 | 2 | 17 |
Ontology | Scale of ABox in Synthetic KBs | Dataset | Ratio | # Subgraphs | ||
---|---|---|---|---|---|---|
# CA | # RA | # A | ||||
Family | 94,176 | 511,514 | 605,690 | train | 0.6 | 56,506 |
valid | 0.2 | 18,835 | ||||
test | 0.2 | 18,835 | ||||
Time | 55,719 | 245,679 | 301,398 | train | 0.6 | 33,432 |
valid | 0.2 | 11,143 | ||||
test | 0.2 | 11,144 |
Ontology | Test Dataset ID | # Subgraphs | # A |
---|---|---|---|
Family | # F1 | 70 | 455 |
# F2 | 196 | 1187 | |
# F3 | 331 | 2127 | |
# F4 | 1722 | 11,020 | |
# F5 | 3618 | 22,913 | |
# F6 | 7196 | 45,746 | |
# F7 | 17,911 | 113,552 | |
# F8 | 35,545 | 226,462 | |
Time | # T1 | 152 | 933 |
# T2 | 525 | 3054 | |
# T3 | 914 | 4933 | |
# T4 | 5003 | 27,755 | |
# T5 | 10,363 | 55,398 | |
# T6 | 20,583 | 111,393 | |
# T7 | 51,947 | 279,038 | |
# T8 | 103,365 | 556,192 |
Method | Ontology | d | HOPE Dimension | t | Batch Size | Epoch |
---|---|---|---|---|---|---|
CFR | Family | 60 | - | 0.5 | 32 | 50 |
Time | 50 | - | 0.5 | 32 | 50 | |
NMT4RDFS | Family | 60 | 4 | - | 32 | 50 |
Time | 50 | 4 | - | 32 | 50 |
Assertion Type | Criterions | CFR | NMT4RDFS | ||
---|---|---|---|---|---|
Family | Time | Family | Time | ||
CA | 0.9428 | - | 0.5102 | - | |
0.9282 | - | 0.4592 | - | ||
0.9354 | - | 0.4834 | - | ||
RA | 0.9652 | 0.9848 | 0.5119 | 0.8166 | |
0.9946 | 0.9164 | 0.5917 | 0.7835 | ||
0.9797 | 0.9493 | 0.5489 | 0.7997 | ||
A | 0.9555 | 0.9848 | 0.5113 | 0.8166 | |
0.9651 | 0.9164 | 0.5329 | 0.7835 | ||
0.9603 | 0.9493 | 0.5218 | 0.7997 |
Ontology | Test Dataset ID | CFR | NMT4RDFS | ||||
---|---|---|---|---|---|---|---|
Family | # F1 | 0.9486 | 0.9986 | 0.9730 | 0.4184 | 0.7437 | 0.5355 |
# F2 | 0.9529 | 0.9979 | 0.9749 | 0.4265 | 0.7026 | 0.5308 | |
# F3 | 0.9498 | 0.9989 | 0.9737 | 0.4668 | 0.7662 | 0.5801 | |
# F4 | 0.9493 | 0.9983 | 0.9732 | 0.4513 | 0.7448 | 0.5620 | |
# F5 | 0.9486 | 0.9986 | 0.9730 | 0.4509 | 0.7466 | 0.5623 | |
# F6 | 0.9496 | 0.9983 | 0.9734 | 0.4555 | 0.7491 | 0.5665 | |
# F7 | 0.9496 | 0.9984 | 0.9734 | 0.4527 | 0.7459 | 0.5634 | |
# F8 | 0.9495 | 0.9984 | 0.9733 | 0.4523 | 0.7453 | 0.5630 | |
Time | # T1 | 0.9824 | 0.9482 | 0.9650 | 0.7850 | 0.8972 | 0.8374 |
# T2 | 0.9800 | 0.9461 | 0.9628 | 0.7865 | 0.8981 | 0.8386 | |
# T3 | 0.9759 | 0.9511 | 0.9633 | 0.7763 | 0.8838 | 0.8266 | |
# T4 | 0.9765 | 0.9493 | 0.9627 | 0.7611 | 0.8783 | 0.8155 | |
# T5 | 0.9783 | 0.9477 | 0.9627 | 0.7737 | 0.8852 | 0.8257 | |
# T6 | 0.9778 | 0.9483 | 0.9628 | 0.7695 | 0.8818 | 0.8219 | |
# T7 | 0.9780 | 0.9481 | 0.9628 | 0.7706 | 0.8826 | 0.8228 | |
# T8 | 0.9778 | 0.9481 | 0.9627 | 0.7699 | 0.8819 | 0.8221 |
Ontology | Test Dataset ID | Time Consumption of Pellet | Time Consumption of HermiT | Time Consumption of the CFR |
---|---|---|---|---|
Family | # F1 | 3 | 1 | 2 |
# F2 | 24 | 3 | 2 | |
# F3 | 65 | 13 | 3 | |
# F4 | 1020 | 742 | 9 | |
# F5 | 5465 | 5339 | 18 | |
# F6 | 22,274 | 39,391 | 34 | |
# F7 | - | - | 83 | |
# F8 | - | - | 163 | |
Time | # T1 | 0.2 | 0.2 | 2 |
# T2 | 0.5 | 0.6 | 3 | |
# T3 | 0.9 | 0.8 | 4 | |
# T4 | 18 | 5 | 18 | |
# T5 | 92 | 12 | 36 | |
# T6 | - | 53 | 71 | |
# T7 | - | 2571 | 176 | |
# T8 | - | 5067 | 355 |
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Zhu, X.; Liu, B.; Zhu, C.; Ding, Z.; Yao, L. Approximate Reasoning for Large-Scale ABox in OWL DL Based on Neural-Symbolic Learning. Mathematics 2023, 11, 495. https://doi.org/10.3390/math11030495
Zhu X, Liu B, Zhu C, Ding Z, Yao L. Approximate Reasoning for Large-Scale ABox in OWL DL Based on Neural-Symbolic Learning. Mathematics. 2023; 11(3):495. https://doi.org/10.3390/math11030495
Chicago/Turabian StyleZhu, Xixi, Bin Liu, Cheng Zhu, Zhaoyun Ding, and Li Yao. 2023. "Approximate Reasoning for Large-Scale ABox in OWL DL Based on Neural-Symbolic Learning" Mathematics 11, no. 3: 495. https://doi.org/10.3390/math11030495
APA StyleZhu, X., Liu, B., Zhu, C., Ding, Z., & Yao, L. (2023). Approximate Reasoning for Large-Scale ABox in OWL DL Based on Neural-Symbolic Learning. Mathematics, 11(3), 495. https://doi.org/10.3390/math11030495