Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a key problem in knowledge representation and databases. This problem can be solved using the chase (aka materialisation) algorithm; however, CQ answering is undecidable for general existential rules, so the chase is not guaranteed to terminate. Several acyclicity conditions provide sufficient conditions for chase termination. In this paper, we present two novel such conditions—model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA)—that generalise many of the acyclicity conditions known so far in the literature. Materialisation provides the basis for several widely-used OWL 2 DL reasoners. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2 DL; furthermore, some systems go beyond OWL 2 RL, but they provide no termination guarantees. In this paper we investigate whether various acyclicity conditions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 DL ontologies are MSA, and that the facts obtained via materialisation are not too large. Thus, our results suggest that principled extensions to materialisationbased OWL 2 DL reasoners may be practically feasible.

Fuzzy description logics (DLs) have been investigated for over two decades, due to their capacity to formalize and reason with imprecise concepts. Very recently, it has been shown that for several fuzzy DLs, reasoning becomes undecidable. Although the proofs of these results differ in the details of each specific logic considered, they are all based on the same basic idea. In this paper, we formalize this idea and provide sufficient conditions for proving undecidability of a fuzzy DL. We demonstrate the effectiveness of our approach by strengthening all previously-known undecidability results and providing new ones. In particular, we show that undecidability may arise even if only crisp axioms are considered.

Belief change studies how to update knowledge bases used for reasoning. Traditionally belief revision has been based on full propositional logic. However, reasoning with full propositional knowledge bases is computationally hard, whereas reasoning with Horn knowledge bases is fast. In the past several years, there has been considerable work in belief revision theory on developing a theory of belief contraction for knowledge represented in Horn form. Our main focus here is the computational complexity of belief contraction, and, in particular, of various methods and approaches suggested in the literature. This is a natural and important question, especially in connection with one of the primary motivations for considering Horn representation: efficiency. The problems considered lead to questions about Horn envelopes (or Horn LUBs), introduced earlier in the context of knowledge compilation. This work gives a syntactic characterization of the remainders of a Horn belief set with respect to a consequence to be contracted, as the Horn envelopes of the belief set and an elementary conjunction corresponding to a truth assignment satisfying a certain explicitly given formula. This gives an efficient algorithm to generate all remainders, each represented by a truth assignment. On the negative side, examples are given of Horn belief sets and consequences where Horn formulas representing the result of contraction, based either on remainders or on weak remainders, must have exponential size for almost all possible choice functions (i.e., different possible choices of partial meet contraction). Therefore using the Horn framework for belief contraction does not by itself give us computational efficiency. Further work is required to explore the possibilities for efficient belief change methods.

Abstract argumentation frameworks (AFs) provide the basis for various reasoning problems in the areas of Knowledge Representation and Artificial Intelligence. Efficient evaluation of AFs has thus been identified as an important research challenge. So far, implemented systems for evaluating AFs have either followed a straight-forward reduction-based approach or been limited to certain tractable classes of AFs. In this work, we present a generic approach for reasoning over AFs, based on the novel concept of complexity-sensitivity. Establishing the theoretical foundations of this approach, we derive several new complexity results for preferred, semistable and stage semantics which complement the current complexity landscape for abstract argumentation, providing further understanding on the sources of intractability of AF reasoning problems. The introduced generic framework exploits decision procedures for problems of lower complexity whenever possible. This allows, in particular, instantiations of the generic framework via harnessing in an iterative way current sophisticated Boolean satisfiability (SAT) solver technology for solving the considered AF reasoning problems. First experimental results show that the SAT-based instantiation of our novel approach outperforms existing systems.

In software testing, the small-scope hypothesis states that a high proportion of errors can be found by testing a program for all test inputs within some small scope. In this paper, we evaluate the small-scope hypothesis for answer-set programming (ASP). To this end, we follow work in traditional testing and base our evaluation on mutation analysis. In fact, we show that a rather limited scope is sufficient for testing ASP encodings from a representative set of benchmark problems. Our experimental evaluation facilitates effective methods for testing in ASP. Also, it gives some justification to analyse programs at the propositional level after grounding them over a small domain.

A counterexample, inconsistency tolerant query answering methods, known now as the Yale Shooting Scenario, showed and mechanisms supporting update operations that early attempts to make the idea of commonsense expressed over the ontology.

We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that produce the largest reduction in empirical conditional entropy; it is greedy in the sense that the choice of addition is based only on the reduction achieved at that iteration. Its sequential nature gives it a lower computational complexity as compared to other existing comparison-based techniques, all of which involve exhaustive searches over every node set of a certain size. Our main result characterizes the sample complexity of this procedure, as a function of node degrees, graph size and girth in factor-graph representation. We subsequently specialize this result to the case of Ising models, where we provide a simple transparent characterization of sample complexity as a function of model and graph parameters. For tree graphs, our algorithm is the same as the classical Chow-Liu algorithm, and in that sense can be considered the extension of the same to graphs with cycles.

We consider the problem of finding the graph on which an epidemic cascade spreads, given only the times when each node gets infected. While this is a problem of importance in several contexts -- offline and online social networks, e-commerce, epidemiology, vulnerabilities in infrastructure networks -- there has been very little work, analytical or empirical, on finding the graph. Clearly, it is impossible to do so from just one cascade; our interest is in learning the graph from a small number of cascades. For the classic and popular "independent cascade" SIR epidemics, we analytically establish the number of cascades required by both the global maximum-likelihood (ML) estimator, and a natural greedy algorithm. Both results are based on a key observation: the global graph learning problem decouples into $n$ local problems -- one for each node. For a node of degree $d$, we show that its neighborhood can be reliably found once it has been infected $O(d^2 \log n)$ times (for ML on general graphs) or $O(d\log n)$ times (for greedy on trees). We also provide a corresponding information-theoretic lower bound of $\Omega(d\log n)$; thus our bounds are essentially tight. Furthermore, if we are given side-information in the form of a super-graph of the actual graph (as is often the case), then the number of cascade samples required -- in all cases -- becomes independent of the network size $n$. Finally, we show that for a very general SIR epidemic cascade model, the Markov graph of infection times is obtained via the moralization of the network graph.

Many methods have been developed to secure the network infrastructure and communication over the Internet. Intrusion detection is a relatively new addition to such techniques. Intrusion detection systems (IDS) are used to find out if someone has intrusion into or is trying to get it the network. One big problem is amount of Intrusion which is increasing day by day. We need to know about network attack information using IDS, then analysing the effect. Due to the nature of IDSs which are solely signature based, every new intrusion cannot be detected; so it is important to introduce artificial intelligence (AI) methods / techniques in IDS. Introduction of AI necessitates the importance of normalization in intrusions. This work is focused on classification of AI based IDS techniques which will help better design intrusion detection systems in the future. We have also proposed a support vector machine for IDS to detect Smurf attack with much reliable accuracy.

We propose a novel algebraic algorithmic framework for dealing with probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem, at a lower computational cost and with higher accuracy. Moreover, the algebraic viewpoint on probability distributions allows us to invoke the theory of algebraic geometry, which we demonstrate in a compact proof for an identifiability criterion.