Related papers: On the Size Complexity and Decidability of First-O…

Constraint propagation is one of the basic forms of inference in many logic-based reasoning systems. In this paper, we investigate constraint propagation for first-order logic (FO), a suitable language to express a wide variety of…

The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…

First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…

Learning and the ability to learn are important factors in development and evolutionary processes [1]. Depending on the level, the complexity of learning can strongly vary. While associative learning can explain simple learning behaviour…

We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…

Regret bounds in online learning compare the player's performance to $L^*$, the optimal performance in hindsight with a fixed strategy. Typically such bounds scale with the square root of the time horizon $T$. The more refined concept of…

In this paper, we study the growth of solutions to higher-order complex linear differential equations in the unit disc, where the analytic coefficients are of finite ({\alpha},\b{eta},{\gamma})-order. By employing the concepts of…

We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…

First-order methods (FOMs) have recently been applied and analyzed for solving problems with complicated functional constraints. Existing works show that FOMs for functional constrained problems have lower-order convergence rates than those…

We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of…

Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…

We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…

This paper is concerned with what intermediate syntactic categories children acquire during first language development, and in what order. Maturational theories make different predictions. Bottom-up accounts (GROWING) propose that lexical…

We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…

We propose a refinement of temporal-difference learning that enforces first-order Bellman consistency: the learned value function is trained to match not only the Bellman targets in value but also their derivatives with respect to states…

Maslov's class $\overline{\text{K}}$ is an expressive fragment of First-Order Logic known to have decidable satisfiability problem, whose exact complexity, however, has not been established so far. We show that $\overline{\text{K}}$ has the…

We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…

For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…