Related papers: Learning Concepts Definable in First-Order Logic w…

The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other.…

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…

We introduce Logical Offline Cycle Consistency Optimization (LOCCO), a scalable, semi-supervised method for training a neural semantic parser. Conceptually, LOCCO can be viewed as a form of self-learning where the semantic parser being…

First-order model counting emerged recently as a novel reasoning task, at the core of efficient algorithms for probabilistic logics. We present a Skolemization algorithm for model counting problems that eliminates existential quantifiers…

We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…

We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even more specifically steady states of BNs. Steady states of BNs…

Structure learning is a core problem in AI central to the fields of neuro-symbolic AI and statistical relational learning. It consists in automatically learning a logical theory from data. The basis for structure learning is mining…

Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years,…

The first-order logical environment FOLE [5] provides a rigorous and principled approach to distributed interoperable first-order information systems. FOLE has been developed in two forms: a classification form and an interpretation form.…

We show that memory-augmented Transformers can implement the entire class of linear first-order methods (LFOMs), a class that contains gradient descent (GD) and more advanced methods such as conjugate gradient descent (CGD), momentum…

First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…

We study the time complexity of the weighted first-order model counting (WFOMC) over the logical language with two variables and counting quantifiers. The problem is known to be solvable in time polynomial in the domain size. However, the…

Rapidly learning abstract concepts from limited examples is a hallmark of human intelligence. This work investigates whether gradient-based meta-learning can equip neural networks with inductive biases for efficient few-shot acquisition of…

We present a unified formalism for structure discovery of causal models and predictive state representation (PSR) models in reinforcement learning (RL) using higher-order category theory. Specifically, we model structure discovery in both…

It was recently shown by van den Broeck at al. that the symmetric weighted first-order model counting problem (WFOMC) for sentences of two-variable logic FO2 is in polynomial time, while it is Sharp-P_1 complete for some FO3-sentences. We…

Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…

A computable structure $\mathcal{A}$ has degree of categoricity $\mathbf{d}$ if $\mathbf{d}$ is exactly the degree of difficulty of computing isomorphisms between isomorphic computable copies of $\mathcal{A}$. Fokina, Kalimullin, and Miller…

Weighted First Order Model Counting (WFOMC) is fundamental to probabilistic inference in statistical relational learning models. As WFOMC is known to be intractable in general ($\#$P-complete), logical fragments that admit polynomial time…

For a sequence of random structures with $n$-element domains over a relational signature, we define its first order (FO) complexity as a certain subset in the Banach space $\ell^{\infty}/c_0$. The well-known FO zero-one law and FO…

It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 ... x_k \#y…