In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: Existing methods for dealing with knowledge updates differ greatly depending on the underlying knowledge representation formalism. When Classical Logic is used, updates are typically performed by manipulating the knowledge base on the model-theoretic level. On the opposite side of the spectrum stand the semantics for updating Answer-Set Programs that need to rely on rule syntax. Yet, a unifying perspective that could embrace both these branches of research is of great importance as it enables a deeper understanding of all involved methods and principles and creates room for their cross-fertilisation, ripening and further development. Furthermore, from a more pragmatic viewpoint, such a unification is a necessary step in addressing updates of hybrid knowledge bases consisting of both a classical and a rule component. This paper bridges the seemingly irreconcilable approaches to updates. It introduces a novel monotonic characterisation of rules, dubbed RE-models, and shows it to be a more suitable semantic foundation for rule updates than SE-models. Then it proposes a generic scheme for specifying semantic rule update operators, based on the idea of viewing a program as the set of sets of RE-models of its rules; updates are performed by introducing additional interpretations exceptions to the sets of RE-models of rules in the original program. The introduced scheme is then used to define particular rule update operators that are closely related to both classical update principles and traditional approaches to rules updates, enjoying a range of plausible syntactic as well as semantic properties. In addition, these operators serve as a basis for a solution to the long-standing problem of state condensing for two of the foundational rule update semantics, showing how they can be equivalently defined as binary operators on some class of logic programs. Finally, the essence of these ideas is extracted to define an abstract framework for exception-based update operators, viewing a knowledge base as the set of sets of models of its elements. It is shown that the framework can capture a wide range of both modeland formula-based classical update operators, and thus serves as the first firm formal ground connecting classical and rule updates.

A: Exception-Based Knowledge Updates
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Q: The success of semi-supervised learning crucially relies on the scalability to a huge amount of unlabelled data that are needed to capture the underlying manifold structure for better classification. Since computing the pairwise similarity between the training data is prohibitively expensive in most kinds of input data, currently, there is no general readyto-use semi-supervised learning method/tool available for learning with tens of millions or more data points. In this paper, we adopted the idea of two low-rank label propagation algorithms, GLNP (Global Linear Neighborhood Propagation) and Kernel Nystrom Approximation, and implemented the parallelized version of the two algorithms accelerated with Nesterov's accelerated projected gradient descent for Big-data Label Propagation (BigLP). The parallel algorithms are tested on five real datasets ranging from 7000 to 10,000,000 in size and a simulation dataset of 100,000,000 samples. In the experiments, the implementation can scale up to datasets with 100,000,000 samples and hundreds of features and the algorithms also significantly improved the prediction accuracy when only a very small percentage of the data is labeled. The results demonstrate that the BigLP implementation is highly scalable to big data and effective in utilizing the unlabeled data for semi-supervised learning.

A: Low-rank Label Propagation for Semi-supervised Learning with 100 Millions Samples
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Q: We proposed Neural Enquirer as a neural network architecture to execute a SQLlike query on a knowledge-base (KB) for answers. Basically, Neural Enquirer finds the distributed representation of a query and then executes it on knowledge-base tables to obtain the answer as one of the values in the tables. Unlike similar efforts in endto-end training of semantic parser [11, 9], Neural Enquirer is fully "neuralized": it not only gives distributional representation of the query and the knowledge-base, but also realizes the execution of compositional queries as a series of differentiable operations, with intermediate results (consisting of annotations of the tables at different levels) saved on multiple layers of memory. Neural Enquirer can be trained with gradient descent, with which not only the parameters of the controlling components and semantic parsing component, but also the embeddings of the tables and query words can be learned from scratch. The training can be done in an end-to-end fashion, but it can take stronger guidance, e.g., the step-by-step supervision for complicated queries, and benefit from it. Neural Enquirer is one step towards building neural network systems which seek to understand language by executing it on real-world. Our experiments show that Neural Enquirer can learn to execute fairly complicated queries on tables with rich structures.

A:
Neural Enquirer: Learning to Query Tables
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