instruction:
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.
question:
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.
answer:
Modularity Aspects of Disjunctive Stable Models

question:
We start with an overview of a class of submodular functions called SCMMs (sums of concave composed with non-negative modular functions plus a final arbitrary modular). We then define a new class of submodular functions we call deep submodular functions or DSFs. We show that DSFs are a flexible parametric family of submodular functions that share many of the properties and advantages of deep neural networks (DNNs), including many-layered hierarchical topologies, representation learning, distributed representations, opportunities and strategies for training, and suitability to GPU-based matrix/vector computing. DSFs can be motivated by considering a hierarchy of descriptive concepts over ground elements and where one wishes to allow submodular interaction throughout this hierarchy. In machine learning and data science applications, where there is often either a natural or an automatically learnt hierarchy of concepts over data, DSFs therefore naturally apply. Results in this paper show that DSFs constitute a strictly larger class of submodular functions than SCMMs, thus justifying their mathematical and practical utility. Moreover, we show that, for any integer k > 0, there are k-layer DSFs that cannot be represented by a k-layer DSF for any k < k. This implies that, like DNNs, there is a utility to depth, but unlike DNNs (which can be universally approximated by shallow networks), the family of DSFs strictly increase with depth. Despite this property, however, we show that DSFs, even with arbitrarily large k, do not comprise all submodular functions. We show this using a technique that "backpropagates" certain requirements if it was the case that DSFs comprised all submodular functions. In offering the above results, we also define the notion of an antitone superdifferential of a concave function and show how this relates to submodular functions (in general), DSFs (in particular), negative second-order partial derivatives, continuous submodularity, and concave extensions. To further motivate our analysis, we provide various special case results from matroid theory, comparing DSFs with forms of matroid rank, in particular the laminar matroid. Lastly, we discuss strategies to learn DSFs, and define the classes of deep supermodular functions, deep difference of submodular functions, and deep multivariate submodular functions, and discuss where these can be useful in applications.
answer:
Deep Submodular Functions

question:
The Swiss avalanche bulletin is produced twice a day in four languages. Due to the lack of time available for manual translation, a fully automated translation system is employed, based on a catalogue of predefined phrases and predetermined rules of how these phrases can be combined to produce sentences. Because this catalogue of phrases is limited to a small sublanguage, the system is able to automatically translate such sentences from German into the target languages French, Italian and English without subsequent proofreading or correction. Having been operational for two winter seasons, we assess here the quality of the produced texts based on two different surveys where participants rated texts from real avalanche bulletins from both origins, the catalogue of phrases versus manually written and translated texts. With a mean recognition rate of 55%, users can hardly distinguish between the two types of texts, and give very similar ratings with respect to their language quality. Overall, the output from the catalogue system can be considered virtually equivalent to a text written by avalanche forecasters and then manually translated by professional translators. Furthermore, forecasters declared that all relevant situations were captured by the system with sufficient accuracy. Forecaster's working load did not change with the introduction of the catalogue: the extra time to find matching sentences is compensated by the fact that they no longer need to double-check manually translated texts. The reduction of daily translation costs is expected to offset the initial development costs within a few years.
answer:
Fully automatic multi-language translation with a catalogue of phrases successful employment for the Swiss avalanche bulletin