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In this study, the authors envisage the neutrosophic number from various distinct rational perspectives and viewpoints to give it a look of a conundrum. They focused and analysed neutrosophic fuzzy numbers when indeterminacy and falsity functions are dependent on each other, which serves an indispensable role for the uncertainty concept. Additionally, the idea of cylindrical neutrosophic single-valued number is focused here, when the indeterminacy and falsity functions are dependent to each other using an influx of different logical and innovative graphical representation. They also developed the score and accuracy function for this particular cylindrical neutrosophic single-valued number and analysed some real-life problems like networking critical path model problem and minimal spanning tree problem of operation research field when the numbers are in cylindrical neutrosophic ambiance. They also introduced a multi-criterion group decision-making problem in this cylindrical neutrosophic domain. This noble thought will help us to solve a plethora of daily life problems in the neutrosophic arena.

Logic-based approaches to legal problem solving model the rule-governed nature of legal argumentation, justification, and other legal discourse but suffer from two key obstacles: the absence of efficient, scalable techniques for creating authoritative representations of legal texts as logical expressions; and the difficulty of evaluating legal terms and concepts in terms of the language of ordinary discourse. Data-centric techniques can be used to finesse the challenges of formalizing legal rules and matching legal predicates with the language of ordinary parlance by exploiting knowledge latent in legal corpora. However, these techniques typically are opaque and unable to support the rule-governed discourse needed for persuasive argumentation and justification. This paper distinguishes representative legal tasks to which each approach appears to be particularly well suited and proposes a hybrid model that exploits the complementarity of each.

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.

We study classes of geometric graphs, which all correspond to the following structural characteristic. For each instance of a vertex set drawn from a universe of possible vertices, each pair of vertices is either required to be connected, forbidden to be connected, or existence or non-existence of an edge is undetermined. The conditions which require or forbid edges are universally quantified predicates defined over the vertex pair, and optionally over existence or non-existence of another edge originating at the vertex pair. We consider further a set of simple graph transformations, where the existence of an edge between two vertices is logically determined by the existence or non-existence of directed edges between both vertices in the original graph. We derive and prove the correctness of a logical expression, which is a necessary and sufficient condition for containedness relations between graph classes that are described this way. We apply the expression on classes of geometric graphs, which are used as theoretical wireless network graph models. The models are constructed from three base class types and intersection combinations of them, with some considered directly and some considered as symmetrized variants using two of the simple graph transformations. Our study then goes systematically over all possible graph classes resulting from those base classes and all possible simple graph transformations. We derive automatically containedness relations between those graph classes. Moreover, in those cases where containedness does not hold, we provide automatically derived counter examples.

Forgetting variables from a propositional formula may increase its size. Introducing new variables is a way to shorten it. Both operations can be expressed in terms of common equivalence, a weakened version of equivalence. In turn, common equivalence can be expressed in terms of forgetting. An algorithm for forgetting and checking common equivalence in polynomial space is given for the Horn case; it is polynomial-time for the subclass of single-head formulae. Minimizing after forgetting is polynomial-time if the formula is also acyclic and variables cannot be introduced, NP-hard when they can.

There are at least two politically salient senses of “representation”—acting-for-others and portraying-something-as-something. The difference is not just semantic but also logical: relations of representative agency are dyadic (x represents y), while portrayals are triadic (x represents y as z). I exploit this insight to disambiguate constructivism and to improve our theoretical vocabulary for analyzing political representation. I amend Saward’s claims-based approach on three points, introducing the “characterization” to correctly identify the elements of representational claims; explaining the “referent” in pragmatic, not metaphysical terms; and differentiating multiple forms of representational activity. This enables me to clarify how the represented can be both prior to representation and constituted by it, and to recover Pitkin’s idea that representatives ought to be “responsive” to the represented. These points are pertinent to debates about the role of representatives, the nature of representative democracy, and the dynamics of revolutionary movements.

Soil organic matter (SOM) stocks, decomposition and persistence are largely the product of controls that act locally. Yet the controls are shaped and interact at multiple spatiotemporal scales, from which macrosystem patterns in SOM emerge. Theory on SOM turnover recognizes the resulting spatial and temporal conditionality in the effect sizes of controls that play out across macrosystems, and couples them through evolutionary and community assembly processes. For example, climate history shapes plant functional traits, which in turn interact with contemporary climate to influence SOM dynamics. Selection and assembly also shape the functional traits of soil decomposer communities, but it is less clear how in turn these traits influence temporal macrosystem patterns in SOM turnover. Here, we review evidence that establishes the expectation that selection and assembly should generate decomposer communities across macrosystems that have distinct functional effects on SOM dynamics. Representation of this knowledge in soil biogeochemical models affects the magnitude and direction of projected SOM responses under global change. Yet there is high uncertainty and low confidence in these projections. To address these issues, we make the case that a coordinated set of empirical practices are required which necessitate (1) greater use of statistical approaches in biogeochemistry that are suited to causative inference; (2) longterm, macrosystem-scale, observational and experimental networks to reveal conditionality in effect sizes, and embedded correlation, in controls on SOM turnover; and (3) use of multiple measurement grains to capture local-and macroscale variation in controls and outcomes, to avoid obscuring causative understanding through data aggregation. When employed together, along with process-based models to synthesize knowledge and guide further empirical work, we believe these practices will rapidly advance understanding of microbial controls on SOM and improve carbon cycle projections that guide policies on climate adaptation and mitigation.

Information on the Internet is fragmented and presented in different data sources, which makes automatic knowledge harvesting and understanding formidable for machines, and even for humans. Knowledge graphs have become prevalent in both of industry and academic circles these years, to be one of the most efficient and effective knowledge integration approaches. Techniques for knowledge graph construction can mine information from either structured, semi-structured, or even unstructured data sources, and finally integrate the information into knowledge, represented in a graph. Furthermore, knowledge graph is able to organize information in an easy-to-maintain, easy-to-understand and easy-to-use manner. In this paper, we give a summarization of techniques for constructing knowledge graphs. We review the existing knowledge graph systems developed by both academia and industry. We discuss in detail about the process of building knowledge graphs, and survey state-of-the-art techniques for automatic knowledge graph checking and expansion via logical inferring and reasoning. We also review the issues of graph data management by introducing the knowledge data models and graph databases, especially from a NoSQL point of view. Finally, we overview current knowledge graph systems and discuss the future research directions.