Related papers: FOLE Equivalence
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
We show that SCL(FOL) can simulate the derivation of non-redundant clauses by superposition for first-order logic without equality. Superposition-based reasoning is performed with respect to a fixed reduction ordering. The completeness…
Pattern-based, modular ontologies have several beneficial properties that lend themselves to FAIR data practices, especially as it pertains to Interoperability and Reusability. However, developing such ontologies has a high upfront cost,…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
Federated learning has emerged as an essential paradigm for distributed multi-source data analysis under privacy concerns. Most existing federated learning methods focus on the ``static" datasets. However, in many real-world applications,…
Building on the classroom framework in Heath et al. (2025), this paper proposes FLARE v2 as a recursive, semiotically informed account of how program meaning can be described across abstraction scales in common teaching languages. It…
We present the Federated Inference Resource Scheduling Toolkit (FIRST), a framework enabling Inference-as-a-Service across distributed High-Performance Computing (HPC) clusters. FIRST provides cloud-like access to diverse AI models, like…
Tabular representation learning has recently gained a lot of attention. However, existing approaches only learn a representation from a single table, and thus ignore the potential to learn from the full structure of relational databases,…
To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning,…
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…
Foundational language models show a remarkable ability to learn new concepts during inference via context data. However, similar work for images lag behind. To address this challenge, we introduce FLoWN, a flow matching model that learns to…
This paper is to introduce an asynchronous and local learning framework for neural networks, named Modular Learning Framework (MOLE). This framework modularizes neural networks by layers, defines the training objective via mutual…
Text-based explanation is a particularly promising approach in explainable AI, but the evaluation of text explanations is method-dependent. We argue that placing the explanations on an information-theoretic framework could unify the…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
Semantic knowledge graphs are foundational to implementing the FAIR Principles, yet RDF/OWL representations often lack the semantic flexibility and cognitive interoperability required in scientific domains. We present a novel framework for…
This paper proposes a reconciliation of two different theories of information. The first, originally proposed in a lesser-known work by Claude Shannon, describes how the information content of channels can be described qualitatively, but…
This paper proposes a theoretical framework which models the information provided by retrieval systems in terms of Information Theory. The proposed framework allows to formalize: (i) system effectiveness as an information theoretic…
Popular machine learning approaches forgo second-order information due to the difficulty of computing curvature in high dimensions. We present FOSI, a novel meta-algorithm that improves the performance of any base first-order optimizer by…
In this paper we describe a new approach to data modelling called the concept-oriented model (CoM). This model is based on the formalism of nested ordered sets which uses inclusion relation to produce hierarchical structure of sets and…