Related papers: Learning Aggregate Queries Defined by First-Order …

Classification of ordinal data is one of the most important tasks of relation learning. In this thesis a novel framework for ordered classes is proposed. The technique reduces the problem of classifying ordered classes to the standard…

The fixed-point logic LREC= was developed by Grohe et al. (CSL 2011) in the quest for a logic to capture all problems decidable in logarithmic space. It extends FO+C, first-order logic with counting, by an operator that formalises a limited…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…

Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…

Within the model-theoretic framework for supervised learning introduced by Grohe and Tur\'an (TOCS 2004), we study the parameterized complexity of learning concepts definable in monadic second-order logic (MSO). We show that the problem of…

Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…

This work reviews how database theory uses tractable circuit classes from knowledge compilation. We present relevant query evaluation tasks, and notions of tractable circuits. We then show how these tractable circuits can be used to address…

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…

Beyond the great cognitive powers showcased by language models, it is crucial to scrutinize whether their reasoning capabilities stem from strong generalization or merely exposure to relevant data. As opposed to constructing increasingly…

Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us…

It has been a long-standing goal in machine learning, as well as in AI more generally, to develop life-long learning systems that learn many different tasks over time, and reuse insights from tasks learned, "learning to learn" as they do…

We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic…

We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…

Combinatorial counting problems pervade artificial intelligence, statistics, and discrete mathematics. Whether the task is enumerating subsets, multisets, permutations, partitions, or compositions under structural and arithmetic…

In recent years crowdsourcing has become the method of choice for gathering labeled training data for learning algorithms. Standard approaches to crowdsourcing view the process of acquiring labeled data separately from the process of…

A parallel method for computing Boolean expressions based on the properties of finite free Boolean algebras is presented. We also show how various finite combinatorial objects can be codded in the formalism of Boolean algebras and counted…

To help a user specify and verify quantified queries --- a class of database queries known to be very challenging for all but the most expert users --- one can question the user on whether certain data objects are answers or non-answers to…

A bounded degree structure is either a relational structure all of whose relations are of bounded degree or a functional structure involving bijective functions only. In this paper, we revisit the complexity of the evaluation problem of not…

Multi-label classification is a common supervised machine learning problem where each instance is associated with multiple classes. The key challenge in this problem is learning the correlations between the classes. An additional challenge…