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.

Input: Consider Input: 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.

Output: Exception-Based Knowledge Updates


Input: Consider Input: 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.

Output: Multiclass Learning Approaches: A Theoretical Comparison with Implications


Input: Consider Input: In security-sensitive applications, the success of machine learning depends on a thorough vetting of their resistance to adversarial data. In one pertinent, well-motivated attack scenario, an adversary may attempt to evade a deployed system at test time by carefully manipulating attack samples. In this work, we present a simple but effective gradientbased approach that can be exploited to systematically assess the security of several, widely-used classification algorithms against evasion attacks. Following a recently proposed framework for security evaluation, we simulate attack scenarios that exhibit different risk levels for the classifier by increasing the attacker’s knowledge of the system and her ability to manipulate attack samples. This gives the classifier designer a better picture of the classifier performance under evasion attacks, and allows him to perform a more informed model selection (or parameter setting). We evaluate our approach on the relevant security task of malware detection in PDF files, and show that such systems can be easily evaded. We also sketch some countermeasures suggested by our analysis.


Output: Evasion attacks against machine learning at test time