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 ...

The interplay between algebraic structures and fuzzy logic has fostered significant advancements in both theoretical research and practical applications. Algebraic structures provide a rigorous ...

This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for ...

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 ...

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 ...