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Knowledge Graphs (KGs) have been applied to many tasks including Web search, link prediction, recommendation, natural language processing, and entity linking. However, most KGs are far from complete and are growing at a rapid pace. To address these problems, Knowledge Graph Completion (KGC) has been proposed to improve KGs by filling in its missing connections. Unlike existing methods which hold a closed-world assumption, i.e., where KGs are fixed and new entities cannot be easily added, in the present work we relax this assumption and propose a new open-world KGC task. As a first attempt to solve this task we introduce an open-world KGC model called ConMask. This model learns embeddings of the entity's name and parts of its text-description to connect unseen entities to the KG. To mitigate the presence of noisy text descriptions, ConMask uses a relationship-dependent content masking to extract relevant snippets and then trains a fully convolutional neural network to fuse the extracted snippets with entities in the KG. Experiments on large data sets, both old and new, show that ConMask performs well in the open-world KGC task and even outperforms existing KGC models on the standard closed-world KGC task.

Knowledge representation learning aims at modeling knowledge graph by encoding entities and relations into a low dimensional space. Most of the traditional works for knowledge embedding need negative sampling to minimize a margin-based ranking loss. However, those works construct negative samples through a random mode, by which the samples are often too trivial to fit the model efficiently. In this paper, we propose a novel knowledge representation learning framework based on Generative Adversarial Networks (GAN). In this GAN-based framework, we take advantage of a generator to obtain high-quality negative samples. Meanwhile, the discriminator in GAN learns the embeddings of the entities and relations in knowledge graph. Thus, we can incorporate the proposed GAN-based framework into various traditional models to improve the ability of knowledge representation learning. Experimental results show that our proposed GAN-based framework outperforms baselines on triplets classification and link prediction tasks.

In recent years, there has been an increasing interest in extending traditional stream processing engines with logical, rule-based, reasoning capabilities. This poses significant theoretical and practical challenges since rules can derive new information and propagate it both towards past and future time points; as a result, streamed query answers can depend on data that has not yet been received, as well as on data that arrived far in the past. Stream reasoning algorithms, however, must be able to stream out query answers as soon as possible, and can only keep a limited number of previous input facts in memory. In this paper, we propose novel reasoning problems to deal with these challenges, and study their computational properties on Datalog extended with a temporal sort and the successor function (a core rule-based language for stream reasoning applications).

Knowledge graphs are useful for many artificial intelligence (AI) tasks. However, knowledge graphs often have missing facts. To populate the graphs, knowledge graph embedding models have been developed. Knowledge graph embedding models map entities and relations in a knowledge graph to a vector space and predict unknown triples by scoring candidate triples. TransE is the first translation-based method and it is well known because of its simplicity and efficiency for knowledge graph completion. It employs the principle that the differences between entity embeddings represent their relations. The principle seems very simple, but it can effectively capture the rules of a knowledge graph. However, TransE has a problem with its regularization. TransE forces entity embeddings to be on a sphere in the embedding vector space. This regularization warps the embeddings and makes it difficult for them to fulfill the abovementioned principle. The regularization also affects adversely the accuracies of the link predictions. On the other hand, regularization is important because entity embeddings diverge by negative sampling without it. This paper proposes a novel embedding model, TorusE, to solve the regularization problem. The principle of TransE can be defined on any Lie group. A torus, which is one of the compact Lie groups, can be chosen for the embedding space to avoid regularization. To the best of our knowledge, TorusE is the first model that embeds objects on other than a real or complex vector space, and this paper is the first to formally discuss the problem of regularization of TransE. Our approach outperforms other state-of-the-art approaches such as TransE, DistMult and ComplEx on a standard link prediction task. We show that TorusE is scalable to large-size knowledge graphs and is faster than the original TransE.

We study query answering in the description logic SQ supporting qualified number restrictions on both transitive and non-transitive roles. Our main contributions are a tree-like model property for SQ-knowledge bases and, building upon this, an optimal automata-based algorithm for answering positive existential regular path queries in 2EXPTIME.

Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning.While incoherence, the non-existence of answer sets for some programs, is an important feature of ASP, it has frequently been criticised and indeed has some disadvantages, especially for query answering.Paracoherent semantics have been suggested as a remedy, which extend the classical notion of answer sets to draw meaningful conclusions also from incoherent programs. In this paper we present an alternative characterization of the two major paracoherent semantics in terms of (extended) externally supported models. This definition uses a transformation of ASP programs that is more parsimonious than the classic epistemic transformation used in recent implementations.A performance comparison carried out on benchmarks from ASP competitions shows that the usage of the new transformation brings about performance improvements that are independent of the underlying algorithms.

Distributions over rankings are used to model user preferences in various settings including political elections and electronic commerce. The Repeated Insertion Model (RIM) gives rise to various known probability distributions over rankings, in particular to the popular Mallows model. However, probabilistic inference on RIM is computationally challenging, and provably intractable in the general case. In this paper we propose an algorithm for computing the marginal probability of an arbitrary partially ordered set over RIM. We analyze the complexity of the algorithm in terms of properties of the model and the partial order, captured by a novel measure termed the "cover width." We also conduct an experimental study of the algorithm over serial and parallelized implementations. Building upon the relationship between inference with rank distributions and counting linear extensions, we investigate the inference problem when restricted to partial orders that lend themselves to efficient counting of their linear extensions.

Dependence is an important concept for many tasks in artificial intelligence. A task can be executed more efficiently by discarding something independent from the task. In this paper, we propose two novel notions of dependence in propositional logic: formula-formula dependence and formula forgetting. The first is a relation between formulas capturing whether a formula depends on another one, while the second is an operation that returns the strongest consequence independent of a formula. We also apply these two notions in two well-known issues: belief update and conservative extension. Firstly, we define a new update operator based on formula-formula dependence. Furthermore, we reduce conservative extension to formula forgetting.

We define a consensus postulate in the propositional belief merging setting. In a nutshell, this postulate imposes the merged base to be consistent with the pieces of information provided by each agent involved in the merging process. The interplay of this new postulate with the IC postulates for belief merging is studied, and an incompatibility result is proved. The maximal sets of IC postulates which are consistent with the consensus postulate are exhibited. When satisfying some of the remaining IC postulates, consensus operators are shown to suffer from a weak inferential power. We then introduce two families of consensus operators having a better inferential power by setting aside some of these postulates.

The study of properties of gradual evaluation methods in argumentation has received increasing attention in recent years, with studies devoted to various classes of frameworks/methods leading to conceptually similar but formally distinct properties in different contexts. In this paper we provide a systematic analysis for this research landscape by making three main contributions. First, we identify groups of conceptually related properties in the literature, which can be regarded as based on common patterns and, using these patterns, we evidence that many further properties can be considered. Then, we provide a simplifying and unifying perspective for these properties by showing that they are all implied by the parametric principles of (either strict or non-strict) balance and monotonicity. Finally, we show that (instances of) these principles are satisfied by several quantitative argumentation formalisms in the literature, thus confirming their general validity and their utility to support a compact, yet comprehensive, analysis of properties of gradual argumentation.

Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufficient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.

We address the issue of quantitatively assessing the severity of inconsistencies in nonmonotonic frameworks. While measuring inconsistency in classical logics has been investigated for some time now, taking the nonmonotonicity into account poses new challenges. In order to tackle them, we focus on the structure of minimal strongly kb-inconsistent subsets of a knowledge base kb---a generalization of minimal inconsistency to arbitrary, possibly nonmonotonic, frameworks. We propose measures based on this notion and investigate their behavior in a nonmonotonic setting by revisiting existing rationality postulates, analyzing the compliance of the proposed measures with these postulates, and by investigating their computational complexity.

AI has seen remarkable progress in recent years, due to a switch from hand-designed shallow representations, to learned deep representations. While these methods excel with plentiful training data, they are still far from the human ability to learn concepts from just a few examples by reusing previously learned conceptual knowledge in new contexts. We argue that this gap might come from a fundamental misalignment between human and typical AI representations: while the former are grounded in rich sensorimotor experience, the latter are typically passive and limited to a few modalities such as vision and text. We take a step towards closing this gap by proposing an interactive, behavior-based model that represents concepts using sensorimotor contingencies grounded in an agent's experience. On a novel conceptual learning and benchmark suite, we demonstrate that conceptually meaningful behaviors can be learned, given supervision via training curricula.

Embedding has emerged as an important approach to prediction, inference, data mining and information retrieval based on knowledge bases and various embedding models have been presented. Most of these models are "typeless," namely, treating a knowledge base solely as a collection of instances without considering the types of the entities therein. In this paper, we investigate the use of entity type information for knowledge base embedding. We present a framework that augments a generic "typeless" embedding model to a typed one. The framework interprets an entity type as a constraint on the set of all entities and let these type constraints induce isomorphically a set of subsets in the embedding space. Additional cost functions are then introduced to model the fitness between these constraints and the embedding of entities and relations. A concrete example scheme of the framework is proposed. We demonstrate experimentally that this framework offers improved embedding performance over the typeless models and other typed models.

The pattern satisfiability is a fundamental problem for SPARQL. This paper provides a complete analysis of decidability/undecidability of satisfiability problems for SPARQL 1.1 patterns. A surprising result is the undecidability of satisfiability for SPARQL 1.1 patterns when only AND and MINUS are expressible. Also, it is shown that any fragment of SPARQL 1.1 without expressing both AND and MINUS is decidable. These results provide a guideline for future SPARQL query language design and implementation.

Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both theoretical and algorithmic perspectives. For the theoretical part, we reduce general MAP inference to its special case without evidence and hidden variables; we also show that it is NP-hard to approximate the MAP problem to 2nε for fixed 0 ≤ ε < 1, where n is the input size. For the algorithmic part, we first present an exact MAP solver that runs reasonably fast and could handle SPNs with up to 1k variables and 150k arcs in our experiments. We then present a new approximate MAP solver with a good balance between speed and accuracy, and our comprehensive experiments on real-world datasets show that it has better overall performance than existing approximate solvers.

Inconsistency-tolerant semantics, like the IAR semantics, have been proposed as means to compute meaningful query answers over inconsistent Description Logic (DL) ontologies. So far query answering under the IAR semantics (IAR-answering) is known to be tractable only for arguably weak DLs like DL-Lite and the quite restricted EL⊥nr fragment of EL⊥. Towards providing a systematic study of IAR-answering, in the current paper we first present a general framework/algorithm for IAR-answering which applies to arbitrary DLs but need not terminate. Nevertheless, this framework allows us to develop a sufficient condition for tractability of IAR-answering and hence of termination of our algorithm. We then show that this condition is always satisfied by the arguably expressive DL DL-Litebool, providing the first positive result for IAR-answering over a non-Horn-DL. In addition, recent results show that this condition usually holds for real-world ontologies and techniques and algorithms for checking it in practice have also been studied recently; thus, overall our results are highly relevant in practice. Finally, we have provided a prototype implementation and a preliminary evaluation obtaining encouraging results.

Existential rules, a family of expressive ontology languages, inherit desired expressive and reasoning properties from both description logics and logic programming. On the other hand, forgetting is a well studied operation for ontology reuse, obfuscation and analysis. Yet it is challenging to establish a theory of forgetting for existential rules. In this paper, we lay the foundation for a theory of forgetting for existential rules by developing a novel notion of unfolding. In particular, we introduce a definition of forgetting for existential rules in terms of query answering and provide a characterisation of forgetting by the unfolding. A result of forgetting may not be expressible in existential rules, and we then capture the expressibility of forgetting by a variant of boundedness. While the expressibility is undecidable in general, we identify a decidable fragment. Finally, we provide an algorithm for forgetting in this fragment.

In this paper, we consider the problem of fair statistical inference involving outcome variables. Examples include classification and regression problems, and estimating treatment effects in randomized trials or observational data. The issue of fairness arises in such problems where some covariates or treatments are "sensitive," in the sense of having potential of creating discrimination. In this paper, we argue that the presence of discrimination can be formalized in a sensible way as the presence of an effect of a sensitive covariate on the outcome along certain causal pathways, a view which generalizes (Pearl 2009). A fair outcome model can then be learned by solving a constrained optimization problem. We discuss a number of complications that arise in classical statistical inference due to this view and provide workarounds based on recent work in causal and semi-parametric inference.

To efficiently answer queries, datalog systems often materialise all consequences of a datalog program, so the materialisation must be updated whenever the input facts change. Several solutions to the materialisation update problem have been proposed. The Delete/Rederive (DRed) and the Backward/Forward (B/F) algorithms solve this problem for general datalog, but both contain steps that evaluate rules "backwards" by matching their heads to a fact and evaluating the partially instantiated rule bodies as queries. We show that this can be a considerable source of overhead even on very small updates. In contrast, the Counting algorithm does not evaluate the rules "backwards," but it can handle only nonrecursive rules. We present two hybrid approaches that combine DRed and B/F with Counting so as to reduce or even eliminate "backward" rule evaluation while still handling arbitrary datalog programs. We show empirically that our hybrid algorithms are usually significantly faster than existing approaches, sometimes by orders of magnitude.

We investigate the relationship between conditional independence (CI) x ⊥ y|Z and the independence of two residuals x – E(x|Z) ⊥ –E(y|Z), where x and y are two random variables, and Z is a set of random variables. We show that if x, y and Z are generated by following linear structural equation model and all external influences follow Gaussian distributions, then x ⊥ y|Z if and only if x – E(x|Z) ⊥ y – E(y|Z). That is, the test of x ⊥ y|Z can be relaxed to a simpler unconditional independence test of x – E(x|Z) ⊥ y – E(y|Z). Furthermore, if all these external influences follow non-Gaussian distributions and the model satisfies structural faithfulness condition, then we have x ⊥ y|Z ⇔ x – E(x|Z) ⊥ y – E(y|Z). We apply the results above to the causal discovery problem, where the causal directions are generally determined by a set of V-structures and their consistent propagations, so CI test-based methods can return a set of Markov equivalence classes. We show that in linear non-Gaussian context, x – E(x|Z) ⊥ y – E(y|Z) ⇒ x – E(x|Z) ⊥ z or y – E(y|Z ⊥ z (∀z ∈ Z) if Z is a minimal d-separator, which implies z causes x (or y) if z directly connects to x (or y). Therefore, we conclude that CIs have useful information for distinguishing Markov equivalence classes. In summary, compared with the existing discretization-based and kernel-based CI testing methods, the proposed method provides a simpler way to measure CI, which needs only one unconditional independence test and two regression operations. When being applied to causal discovery, it can find more causal relationships, which is experimentally validated.

A number of proposals have been made to define inconsistency measures. Each has its rationale. But to date, it is not clear how to delineate the space of options for measures, nor is it clear how we can classify measures systematically. In this paper, we introduce a general framework for comparing syntactic inconsistency measures. It uses the construction of an inconsistency graph for each knowledgebase. We then introduce abstractions of the inconsistency graph and use the hierarchy of the abstractions to classify a range of inconsistency measures.

We provide formal definitions of degree of blameworthiness and intention relative to an epistemic state (a probability over causal models and a utility function on outcomes). These, together with a definition of actual causality, provide the key ingredients for moral responsibility judgments. We show that these definitions give insight into commonsense intuitions in a variety of puzzling cases from the literature.

Conditional information is an integral part of representation and inference processes of causal relationships, temporal events, and even the deliberation about impossible scenarios of cognitive agents. For formalizing these inferences, a proper formal representation is needed. Psychological studies indicate that classical, monotonic logic is not the approriate model for capturing human reasoning: There are cases where the participants systematically deviate from classically valid answers, while in other cases they even endorse logically invalid ones. Many analyses covered the independent analysis of individual inference rules applied by human reasoners. In this paper we define inference patterns as a formalization of the joint usage or avoidance of these rules. Considering patterns instead of single inferences opens the way for categorizing inference studies with regard to their qualitative results. We apply plausibility relations which provide basic formal models for many theories of conditionals, nonmonotonic reasoning, and belief revision to asses the rationality of the patterns and thus the individual inferences drawn in the study. By this replacement of classical logic with formalisms most suitable for conditionals, we shift the basis of judging rationality from compatibility with classical entailment to consistency in a logic of conditionals. Using inductive reasoning on the plausibility relations we reverse engineer conditional knowledge bases as explanatory model for and formalization of the background knowledge of the participants. In this way the conditional knowledge bases derived from the inference patterns provide an explanation for the outcome of the study that generated the inference pattern.

With the recent development of deep learning, research in AI has gained new vigor and prominence. While machine learning has succeeded in revitalizing many research fields, such as computer vision, speech recognition, and medical diagnosis, we are yet to witness impressive progress in natural language understanding. One of the reasons behind this unmatched expectation is that, while a bottom-up approach is feasible for pattern recognition, reasoning and understanding often require a top-down approach. In this work, we couple sub-symbolic and symbolic AI to automatically discover conceptual primitives from text and link them to commonsense concepts and named entities in a new three-level knowledge representation for sentiment analysis. In particular, we employ recurrent neural networks to infer primitives by lexical substitution and use them for grounding common and commonsense knowledge by means of multi-dimensional scaling.