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]: Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where fully declarative and nonmonotonic languages are applied. In this context, obtaining a modular structure for programs is by no means straightforward since the output of an entire program cannot in general be composed from the output of its components. To better understand the effects of disjunctive information on modularity we restrict the scope of analysis to the case of disjunctive logic programs (DLPs) subject to stable-model semantics. We define the notion of a DLP-function, where a well-defined input/output interface is provided, and establish a novel module theorem which indicates the compositionality of stable-model semantics for DLP-functions. The module theorem extends the well-known splitting-set theorem and enables the decomposition of DLP-functions given their strongly connected components based on positive dependencies induced by rules. In this setting, it is also possible to split shared disjunctive rules among components using a generalized shifting technique. The concept of modular equivalence is introduced for the mutual comparison of DLP-functions using a generalization of a translation-based verification method.
[A]: Modularity Aspects of Disjunctive Stable Models


[Q]: We theoretically analyze and compare the following five popular multiclass classification methods: One vs. All, All Pairs, Tree-based classifiers, Error Correcting Output Codes (ECOC) with randomly generated code matrices, and Multiclass SVM. In the first four methods, the classification is based on a reduction to binary classification. We consider the case where the binary classifier comes from a class of VC dimension d, and in particular from the class of halfspaces over R. We analyze both the estimation error and the approximation error of these methods. Our analysis reveals interesting conclusions of practical relevance, regarding the success of the different approaches under various conditions. Our proof technique employs tools from VC theory to analyze the approximation error of hypothesis classes. This is in sharp contrast to most, if not all, previous uses of VC theory, which only deal with estimation error.
[A]: Multiclass Learning Approaches: A Theoretical Comparison with Implications


[Q]: Assessing the degree of semantic relatedness between words is an important task with a variety of semantic applications, such as ontology learning for the Semantic Web, semantic search or query expansion. To accomplish this in an automated fashion, many relatedness measures have been proposed. However, most of these metrics only encode information contained in the underlying corpus and thus do not directly model human intuition. To solve this, we propose to utilize a metric learning approach to improve existing semantic relatedness measures by learning from additional information, such as explicit human feedback. For this, we argue to use word embeddings instead of traditional high-dimensional vector representations in order to leverage their semantic density and to reduce computational cost. We rigorously test our approach on several domains including tagging data as well as publicly available embeddings based on Wikipedia texts and navigation. Human feedback about semantic relatedness for learning and evaluation is extracted from publicly available datasets such as MEN or WS-353. We find that our method can significantly improve semantic relatedness measures by learning from additional information, such as explicit human feedback. For tagging data, we are the first to generate and study embeddings. Our results are of special interest for ontology and recommendation engineers, but also for any other researchers and practitioners of Semantic Web techniques.
[A]:
Learning Semantic Relatedness from Human Feedback Using Metric Learning