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Collaborative filtering (CF) is a central solution for capturing various user-item relationships in building recommender systems. However, when the relationships are sparsely observed, it is challenging to obtain enough signals to infer precise user preferences. Recent studies have attempted to address the sparsity issue by incorporating multimodal information (e.g., image and text) into CF models. However, existing methods mainly focus on capturing modal-specific user preference with multiple unimodal graphs, ignoring the complex nature of user behavior, which is determined by an intricate fusion of multimodal information. Therefore, we develop a Self-supervised Multimodal Graph Convolutional Network (SMGCN), which aims to learn the cross-modal user preferences over multiple modalities with an expressive multimodal fusion on a single graph. More importantly, to facilitate and enhance multimodal fusion in SMGCN, we devise two novel self-supervised learning techniques. 1) Collaborative Multimodal Alignment (CMA) uses contrastive learning to align the domain-specific multimodal semantics with the user-item relational semantics. 2) Multimodal Consistency Regularization (MCR) alleviates the sensitivity on a certain modality and increases model robustness. The experimental results demonstrate that our model consistently outperforms advanced multimodal models on three benchmark datasets. • We propose Self-supervised Multimodal Graph Convolutional Network (SMGCN) for cross-modal user preferences. • Introducing key self-supervisory methods for enhanced multimodal fusion in collaborative filtering: CMA and MCR. • We demonstrated that the proposed SMGCN outperforms top-K recommendation baselines in three real-world datasets. [ABSTRACT FROM AUTHOR]

Abstract Multi-valued model checking has been studied extensively recently, but important uncertain information contained in systems of multi-valued logics has not been considered in previous work and, as a consequence, some serious deficiencies arise. To make up for these deficiencies, this paper considers the possibility information implied in multi-valued systems. Precisely, we investigate computation tree logic model checking based on multi-valued possibility measures. We model multi-valued logic systems by multi-valued Kripke structures (MvKSs) and specify their verification properties by multi-valued computation tree logic (MvCTL) formulae. Based on generalized possibility measures and generalized necessity measures, an MvCTL model checking method is proposed, the pseudocode of the corresponding model checking algorithm is presented, and its time complexity is analyzed in detail. Furthermore, after detailed comparisons with χ CTL (introduced in Chechik et al. [10]) and the classical CTL, we show that MvCTL is more general than χ CTL, but cannot be reduced to the classical CTL. The conditions on lattice and MvKS under which MvCTL is equivalent to χ CTL are given. Finally, some examples and a case study are given to illustrate the MvCTL model-checking method. [ABSTRACT FROM AUTHOR]