Related papers: Advances in Algorithmic Meta Theorems

In the last years, enumeration algorithms with bounded delay have attracted a lot of attention for several data management tasks. Given a query and the data, the task is to preprocess the data and then enumerate all the answers to the query…

We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in…

Tarski initiated a logic-based approach to formal geometry that studies first-order structures with a ternary betweenness relation \beta, and a quaternary equidistance relation \equiv. Tarski established, inter alia, that the first-order…

Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…

Real-world problems are becoming highly complex and, therefore, have to be solved with combinatorial optimisation (CO) techniques. Motivated by the strong increase of publications on CO, 8,393 articles from this research field are subjected…

We conjecture that the relative unpopularity of logical frameworks among practitioners is partly due to their complex meta-languages, which often demand both programming skills and theoretical knowledge of the meta-language in question for…

Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…

The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…

We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class C of finite structures that can be…

Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

Relevant combinatorial optimization problems (COPs) are often NP-hard. While they have been tackled mainly via handcrafted heuristics in the past, advances in neural networks have motivated the development of general methods to learn…

We present a fixed-parameter tractable algorithm for first-order model checking on interpretations of graph classes with bounded local cliquewidth. Notably, this includes interpretations of planar graphs, and more generally, of classes of…

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this…

Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences. Despite…

Large Language Models (LLMs) have achieved impressive results in processing text data, which has sparked interest in applying these models beyond textual data, such as graphs. In the field of graph learning, there is a growing interest in…

Two major areas of interest in the era of Large Language Models regard questions of what do LLMs know, and if and how they may be able to reason (or rather, approximately reason). Since to date these lines of work progressed largely in…

Neural Combinatorial Optimization approaches have recently leveraged the expressiveness and flexibility of deep neural networks to learn efficient heuristics for hard Combinatorial Optimization (CO) problems. However, most of the current…

Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…

Large language models (LLMs) are increasingly evaluated on reasoning tasks, yet their logical abilities remain contested. To address this, we study LLMs' reasoning in a well-defined fragment of logic: syllogistic reasoning. We cast the…