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The purpose of this article is to study the algorithmic complexity of the Besicovitch stability of noisy subshifts of finite type, a notion studied in a previous article. First, we exhibit an unstable aperiodic tiling, and then see how it…

In process mining, alignments quantify the degree of deviation between an observed event trace and a business process model and constitute the most important conformance checking technique. We study the algorithmic complexity of computing…

Nowadays, scientific databases have become the bread-and-butter of particle physicists. These databases must be maintained and checked repeatedly to insure the accuracy of their content. The COMPETE collaboration aims at motivating data…

Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of…

Equipping machines with comprehensive knowledge of the world's entities and their relationships has been a long-standing goal of AI. Over the last decade, large-scale knowledge bases, also known as knowledge graphs, have been automatically…

We consider here the problem of obtaining reliable, consistent information from inconsistent databases -- databases that do not have to satisfy given integrity constraints. We use the notion of consistent query answer -- a query answer…

A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…

In this paper, we focus on the problem of existence and computing of small and large stable models. We show that for every fixed integer k, there is a linear-time algorithm to decide the problem LSM (large stable models problem): does a…

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…

A knowledge system S describing a part of real world does in general not contain complete information. Reasoning with incomplete information is prone to errors since any belief derived from S may be false in the present state of the world.…

We show that many classical decision problems about 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are $\Pi_2^1$-complete, hence located at the second level of the analytical hierarchy, and…

A common practice of ML systems development concerns the training of the same model under different data sets, and the use of the same (training and test) sets for different learning models. The first case is a desirable practice for…

The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…

This article describes an approach to modeling knowledge acquisition in terms of walks along complex networks. Each subset of knowledge is represented as a node, and relations between such knowledge are expressed as edges. Two types of…

Evaluating conjunctive queries and solving constraint satisfaction problems are fundamental problems in database theory and artificial intelligence, respectively. These problems are NP-hard, so that several research efforts have been made…

Representation learning of knowledge bases (KBs) aims to embed both entities and relations into a low-dimensional space. Most existing methods only consider direct relations in representation learning. We argue that multiple-step relation…

Knowledge tracing (KT) is a fundamental task in educational data mining that mainly focuses on students' dynamic cognitive states of skills. The question-answering process of students can be regarded as a thinking process that considers the…

Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…

Concept-based Models are a class of inherently explainable networks that improve upon standard Deep Neural Networks by providing a rationale behind their predictions using human-understandable `concepts'. With these models being highly…