Hallucination is fundamental to how transformer-based language models work. In fact, it’s their greatest asset: this is the method by which language models find links between sometimes disparate ...

Algebraic logic constitutes a vibrant interdisciplinary field that investigates the close interplay between algebraic structures and logical systems. By utilising tools from universal algebra, ...

Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

Tech stock declines highlight unsustainable AI spending; EssentaTor proposes Mapping Mathematics for durable, efficient intelligence systems.

Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...

Microsoft has introduced a new set of small language models called Phi-4-reasoning, Phi-4-reasoning-plus, and Phi-4-mini-reasoning, which are described as "marking a new era for efficient AI." These ...