Representation and Reasoning of Three-Dimensional Spatial Relationships Based on R5DOS-Intersection Model Representation and Reasoning Based on R5DOS Model

Abstract

This paper aims to disclose the compound topological and directional relationships of three simple regions in the three-dimensional (3D) space. For this purpose, the directional model and the 8-intersection model were coupled into an R5DOS-intersection model and used to represent three simple regions in the 3D space. The matrices represented by the model were found to be complete and mutually exclusive. Then, a self-designed algorithm was adopted to solve the model, yielding 11,038 achievable topological and directional relationships. Compared with the minimum bounding rectangle (MBR) model, the proposed model boasts strong expressive power. Finally, our model was applied to derive the topological and directional relationships between simple regions A and C from the known relationships between simple regions A and B and those between B and C. Based on the results, a compound relationship reasoning table was established for A and C. The research results shed new light on the representation and reasoning of 3D spatial relationships.

Self-Consistent Narrative Prompts on Abductive Natural Language Inference

“…Apart from incorporating commonsense knowledge to tackle this task, Zhu et al (2020) reformulated the αNLI task as a ranking task using a learning-toranking framework to rank candidate hypotheses. Li et al (2021a) proposed an interactive language model that groups the correct and incorrect hypotheses instead of ranking these hypotheses and adopts joint softmax focal loss for this αNLI task. However, prior works did not exploit model consistency and various narrative sequences in this task.…”

“…The implementation detail of α-PACE is displayed in Appendix A.2, and we compare α-PACE with two categories of competitive baselines. The first category is the previous state-of-the-art (SOTA) baselines, such as BERT (Devlin et al, 2019), RoBERTa (Liu et al, 2019), DeBERTa (He et al, 2021), McQueen (Mitra et al, 2019), MHKA (Paul et al, 2020), ege-RoBERTa-large (Du et al, 2021), L2R 2 (Zhu et al, 2020), IMSL (Li et al, 2021a), UNIMO (Li et al, 2021b), and UNICORN (T5) (Lourie et al, 2021). Another category of baselines is T5-based models, and we include the fine-tuned T5 model to illustrate the performance gain of our model.…”

“…Random -50.40 BERT (Devlin et al, 2019) 69.10 68.90 RoBERTa (Liu et al, 2019) 85.76 84.48 McQueen (Mitra et al, 2019) 86.68 -MHKA (Paul et al, 2020) 87.44 87.12 ege-RoBERTa (Du et al, 2021) -87.50 L2R 2 (Zhu et al, 2020) 88.44 86.11 RoBERTa-L+IMSL (Li et al, 2021a) 89.20 -Prefix-Tuning (T5) (Lester et al, 2021) 84.20 83.88 Prompt-Tuning (T5) (Li and Liang, 2021) 86.23 85.98 Fine-Tuning (T5) (Raffel et al, 2020) 87 methods such as Prefix-Tuning (T5) (Li and Liang, 2021) and Prompt-Tuning (T5) (Lester et al, 2021) are included as baselines for exhibiting the exact contribution of our proposed method. The implementation details of the T5 fine-tuning model are described in Appendix A.3, while Prefix-Tuning and Prompt-Tuning methods are appended in Appendix A.4.…”

“…Traditional works on the αNLI task focus on ranking the hypotheses among "H 1 " and "H 2 " (Zhu et al, 2020;Li et al, 2021a) or incorporating the knowledge from various sources into pre-trained language models, such as general commonsense knowledge (Mitra et al, 2019;Du et al, 2021) and social commonsense knowledge (Paul et al, 2020). However, one crucial piece of information, i.e., the inter-sentential coherence and the consistency of the model, has yet to be investigated and explored.…”

Leader-Follower UAV Formation Model Based on R5DOS-Intersection Model

“…In 2020, Li et al [19] proposed a three-dimensional topology-azimuth compound relationship model R5DOS model based on RCC-5 theory and an eight-direction cone model. This model fills the research deficiencies in the field of compound relational models in three-dimensional space.…”