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A non-distributive two-sorted hypersequent calculus PDBL and its modal extension MPDBL are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational semantics for PDBL is next proposed, where any formula is interpreted as a semiconcept of a context. For MPDBL , the relational semantics is based on Kripke contexts, and a formula is interpreted as a semiconcept of the underlying context. The systems are shown to be sound and complete with respect to the relational semantics. Adding appropriate sequents to MPDBL results in logics with semantics based on reflexive, symmetric or transitive Kripke contexts. In particular, one gets the logics MPDBL4 and MPDBL5 with semantics respectively based on reflexive, transitive Kripke contexts and reflexive, symmetric and transitive Kripke contexts. MPDBL4 also happens to be the logic for topological pure double Boolean algebra. It is demonstrated that, using PDBL , the basic notions and relations of conceptual knowledge can be expressed and inferences involving negations can be obtained. Further, drawing a connection with rough set theory, lower and upper approximations of semiconcepts of a context are defined. It is then shown that, using the formulae and sequents involving modal operators in MPDBL5 , these approximation operators and their properties can be captured. [ABSTRACT FROM AUTHOR]

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]

Following K. Segerberg [22] , D. Kozen [15] and V. Pratt [19] , who have been introduced dynamic propositional logic and dynamic algebras, dynamic propositional Łukasiewicz logic DP Ł (dynamic n -valued propositional Łukasiewicz logic D P Ł n) and dynamic MV -algebras (dynamic M V n -algebras) are introduced and theories of the logic DP Ł (D P Ł n) and dynamic MV -algebras (M V n -algebras) are developed. Dynamic MV -algebras (dynamic M V n -algebras) are algebraic counterparts of the logic DP Ł (D P Ł n), that in turn represent two-sorted algebras that combine the varieties of MV -algebras (M V n -algebras) (M , ⊕ , ⊙ , ∼ , 0 , 1) and regular algebras (R , ∪ , ; , ⁎) into a single finitely axiomatized variety (M , R , ◇) resembling R -module with "scalar" multiplication ◇. Kripke semantics is developed for dynamic propositional Łukasiewicz logic (dynamic n -valued propositional Łukasiewicz logic D P Ł n). [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]

Cardiff University, Cardiff, United Kingdom, Europe, Experimental Psychology The news correspondents obtained a quote from the research from Cardiff University: "In particular, we demonstrate a reversal of the classical, well-replicated symbolic distance effect (SDE), as a function of relational semantics. Keywords: Cardiff University; Cardiff; United Kingdom; Europe; Experimental Psychology EN Cardiff University Cardiff United Kingdom Europe Experimental Psychology Investigators publish new report on experimental psychology. [Extracted from the article]

Keywords for this news article include: Milan, Italy, Europe, Automated Reasoning, Calculi, Health and Medicine, University of Milano Bicocca. Keywords: Milan; Italy; Europe; Automated Reasoning; Calculi; Health and Medicine EN Milan Italy Europe Automated Reasoning Calculi Health and Medicine 7223 7223 1 03/23/23 20230310 NES 230310 2023 MAR 10 (NewsRx) -- By a News Reporter-Staff News Editor at Health & Medicine Week -- New research on Automated Reasoning is the subject of a report. Italy, Europe, Automated Reasoning, Milan, Health and Medicine, Calculi. [Extracted from the article]

This paper introduces and studies extensions of modal logics by investigating the soundness of classical modal axioms in a weighted framework. It discusses the notion of relevant weight values, in a specific weighted Kripke semantics and exploits accessibility relation properties. Different generalisations of the classical axioms are constructed and, from these, a typology of weighted axioms is built, distinguishing between four types, depending on their relations to their classical counterparts and to the, possibly equivalent, frame conditions. [ABSTRACT FROM AUTHOR]

Abstract: During the last decades, a large amount of multi-valued transition systems, whose transitions or states are labeled with specific weights, have been proposed to analyze quantitative behaviors of reactive systems. To set up a unified framework to model and analyze systems with quantitative information, in this paper, we present an extension of doubly labeled transition systems in the framework of residuated lattices, which we will refer to as lattice-valued doubly labeled transition systems (LDLTSs). Our model can be specialized to fuzzy automata over complete residuated lattices, fuzzy transition systems, and multi-valued Kripke structures. In contrast to the traditional yes/no approach to similarity, we then introduce lattice-valued similarity between LDLTSs to measure the degree of closeness of two systems, which is a value from a residuated lattice. Further, we explore the properties of robustness and compositionality of the lattice-valued similarity. Finally, we extend the Hennessy–Milner logic to the residuate lattice-valued setting and show that the obtained logic is adequate and expressive with lattice-valued similarity. [Copyright &y& Elsevier]