Outlier detection by logic programming

We show that stable models of logic programs may be viewed as minimal models of programs that satisfy certain additional constraints. To do so, we transform the normal programs into disjunctive logic programs and sets of integrity constraints. We show that the stable models of the normal program coincide with the minimal models of the disjunctive program thatsatisfy the integrity constraints. As a consequence, the stable model semantics can be characterized using theextended generalized closed world assumption for disjunctive logic programs. Using this result, we develop a bottomup algorithm for function-free logic programs to find all stable models of a normal program by computing the perfect models of a disjunctive stratified logic program and checking them for consistency with the integrity constraints. The integrity constraints provide a rationale as to why some normal logic programs have no stable models.

The outlier detection problem has important applications in the field of fraud detection, network robustness analysis, and intrusion detection. Most such applications are high dimensional domains in which the data can contain hundreds of dimensions. Many recent algorithms use concepts of proximity in order to find outliers based on their relationship to the rest of the data. However, in high dimensional space, the data is sparse and the notion of proximity fails to retain its meaningfulness. In fact, the sparsity of high dimensional data implies that every point is an almost equally good outlier from the perspective of proximity-based definitions. Consequently, for high dimensional data, the notion of finding meaningful outliers becomes substantially more complex and non-obvious. In this paper, we discuss new techniques for outlier detection which find the outliers by studying the behavior of projections from the data set.

This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond–Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al. (2007), which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.

M. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated by Rondogiannis and Symeonidou that Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values. Rondogiannis and Symeonidou also demonstrated that Bezem's technique, when extended under the stable model semantics, does not in general lead to extensional stable models. In this paper, we consider the problem of extending Bezem's technique under the well-founded semantics. We demonstrate that the well-founded extensionfailsto retain extensionality in the general case. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved. We analyze the reasons of the failure of extensionality in the general case, arguing that a three-valued setting cannot distinguish between certain predicates that appear to have a different behaviour inside a program context, but which happen to be identical as three-valued relations.

With the widespread use of closed-circuit television (CCTV) surveillance systems in public areas, crowd anomaly detection has become an increasingly critical aspect of the intelligent video surveillance system. It requires workforce and continuous attention to decide on the captured event, which is hard to perform by individuals. The available literature on human action detection includes various approaches to detect abnormal crowd behavior, which is articulated as an outlier detection problem. This paper presents a detailed review of the recent development of anomaly detection methods from the perspectives of computer vision on different available datasets. A new taxonomic organization of existing works in crowd analysis and anomaly detection has been introduced. A summarization of existing reviews and datasets related to anomaly detection has been listed. It covers an overview of different crowd concepts, including mass gathering events analysis and challenges, types of anomalies, and surveillance systems. Additionally, research trends and future work prospects have been analyzed.

We present many-valued disjunctive logic programs in which classical disjunctive logic program clauses are extended by a truth value that respects the material implication. Interestingly, these many-valued disjunctive logic programs have both a probabilistic semantics in probabilities over possible worlds and a truth-functional semantics. We then define minimal, perfect, and stable models and show that they have the same properties like their classical counterparts. In particular, perfect and stable models are always minimal models. Under local stratification, the perfect model semantics coincides with the stable model semantics. Finally, we show that some special cases of propositional many-valued disjunctive logic programming under minimal, perfect, and stable model semantics have the same complexity like their classical counterparts.

We propose C4, a four-valued semantics for normal, logic programs. Using this semantics, we define two types of entailment: strong and weak. We show that a normal, logic program strongly entails a sentence under C4 if, and only if, the program entails that sentence under the well founded semantics and it weakly entails a sentence if, and only if, the program entails that sentence under the two-valued stable model semantics in case the program has any stable models. We argue that this shows that the difference between the well founded semantics and the stable model semantics can be characterized in terms of their attitude to what we call contested information. We use this insight to propose a general theory of contested reasoning.

In recent years, anomaly detection techniques in time-series data have been widely used in manufacturing, cybersecurity, and other fields. Meanwhile, various anomaly detection models based on generative adversarial networks (GAN) are gradually used in time-series anomaly detection tasks. However, there are problems of unstable generator training, missed detection of anomalous data, and inconsistency between the discriminator's discriminant and the anomaly detection target in GAN networks. Aiming at the above problems, the paper proposes a DUAL-ADGAN (Dual Anomaly Detection Generative Adversarial Networks) model for the detection of anomalous data in time series. First, the Wasserstein distance satisfying the Lipschitz constraint is used as the loss function of the data reconstruction module, which improves the stability of the traditional GAN network training. Second, by adding a data prediction module to the DUAL-ADGAN model, the distinction between abnormal and normal samples is increased, and the rate of missing abnormal data in the model is reduced. Third, by introducing the Fence-GAN loss function, the discriminator is aligned with the anomaly detection target, which effectively reduces the anomaly data false detection rate of the DUAL-ADGAN model. Finally, anomaly scores derived from the DUAL-ADGAN model are compared with dynamic thresholds to detect anomalies. The experimental results show that the average F1 of the DUAL-ADGAN model is 0.881, which is better than the other nine baseline models. The conclusions demonstrate that the DUAL-ADGAN model proposed in the paper is more stable in training while effectively solving the problems of anomaly miss detection and discriminator inconsistency with the anomaly detection target in the anomaly detection task.

We define abstract proof procedures for performing credulous and sceptical non-monotonic reasoning, with respect to the argumentation-theoretic formulation of non-monotonic reasoning proposed in [1]. Appropriate instances of the proposed proof procedures provide concrete proof procedures for concrete formalisms for non-monotonic reasoning, for example logic programming with negation as failure and default logic.We propose (credulous and sceptical) proof procedures under different argumentation-theoretic semantics, namely the conventional stable model semantics and the more liberal partial stable model or preferred extension semantics. We study the relationships between proof procedures for different semantics, and argue that, in many meaningful cases, the (simpler) proof procedures for reasoning under the preferred extension semantics can be used as sound and complete procedures for reasoning under the stable model semantics. In many meaningful cases still, proof procedures for credulous reasoning under the preferred extension semantics can be used as (much simpler) sound and complete procedures for sceptical reasoning under the preferred extension semantics. We compare the proposed proof procedures with existing proof procedures in the literature.

Restricted default theories: Expressive power and outlier detection tasks

OHODIN is an online extension for data streams of the kNN-based ODIN anomaly detection approach. It provides a detection-threshold heuristic that is based on extreme value theory. In contrast to sophisticated anomaly and novelty detection approaches the decision-making process of ODIN is interpretable by humans, making it interesting for certain applications. However, it is limited in terms of the underlying detection method. In this article, we present an extension of the OHODIN to further detection techniques to reinforce OHODIN capability of online data streams anomaly detection. We introduce the algorithm modifications and an experimental evaluation with competing state-of-the-art anomaly detection approaches.

We present a model for deductive object oriented query languages with inheritance and overriding. In this model, we consider a DAG like dynamic isa hierarchy and we account for both value or attribute inheritance and method inheritance or code sharing. We show that these two types of inheritance can be treated uniformly within an elegant declarative setting. We then propose a novel semantics for the non-monotonic behavior resulting from the combination of overriding, dynamic selfbinding and the dynamic structure of the isa hierarchy. This semantics is reminiscent of the stable model semantics of logic programs with negation. We also isolate a syntactic condition that guarantees the existence of a unique stable model for a program. This condition, in its turn, is inspired by the local stratification condition of perfect model semantics for programs with negation. Finally we define a bottom-up procedure that computes the unique stable model of a stratified program.KeywordsLogic ProgramLogic ProgrammingStable ModelUnit ClauseStable Model SemanticThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The paper presents the problem of outlier detection in the rule knowledge bases. Unusual (rare) rules, regarded here as the deviation, should be the subject of analysis experts and knowledge engineers because they can influence the efficiency of inference in decision support systems. The author presents a different approach in finding outliers in the rules. The experiments with their results are also presented in the paper.

Anomalies in data may be caused by errors in the data, but sometimes the appearance of anomalous data often also suggests the emergence of a new domain or a new underlying process. Anomaly detection has therefore been an active area of research for decades. This paper is based on what anomaly detection is, the main areas of application for anomaly detection, and the challenges of anomaly detection at this stage. Deep learning-based anomaly detection is proposed based on the unpredictability, diversity, and sparsity that exist in anomaly detection, and deep learning anomaly detection algorithms are classified into unsupervised deep anomaly detection algorithms and semi-supervised deep anomaly detection algorithms based on the use of anomaly labels. This paper reviews and analyses the research on these two algorithms, and elaborates on the advantages and disadvantages of each type of anomaly detection algorithm when applied. Deep anomaly detection is also applied to the anomaly detection of charging data and is classified according to the different types of charging data, into deep anomaly detection for electric vehicles, deep anomaly detection for charging stations, and deep anomaly detection for charging poles. Finally, we provide an outlook on various algorithms for anomaly detection and future applications of anomaly detection in charging data.

In terms of the arithmetic hierarchy, the complexity of the set of minimal models and of the set of stable models of a propositional general logic program has previously been described. However, not every set of interpretations of this level of complexity is obtained as such a set. In this paper we identify the sets of interpretations which are minimal or stable model classes by their properties in an appropriate topology on the space of interpretations. Closely connected with the topological characterization, in parallel with results previously known for stable model classes we obtain for minimal model classes both a normal-form representation as the set of minimal models of a prerequisite-free program and a logical description in terms of formulas. Our approach centers on the relation which we establish between stable and minimal model classes. We include examples of calculations which can be performed by these methods. Let P be a propositional general logic program over a finite or countably infinite set U of atoms. Recall that an interpretation for P is a subset of U. By a model of P we mean an interpretation S c_ U which is closed under Te; by a minimal model of P we mean a model S of P such that no proper subset S' ~ S is a model of P; and by a stable model of P we mean a set S _C U such that S = least fixpoint of T~Ls(t,), where GLs(P) is the Gelfond-Lifschit z transform of program P with respect to S defined in [3]. Let Mod(P), Min(P), and Stab(P) denote, respectively, the set of models, minimal models, and stable models of P. For a given program P, we see that these classes are related by