This is a preview. Log in through your library . Abstract This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the ...

We solve a problem of Friedman by showing the existence of a logic stronger than first-order logic even for countable models, but still satisfying the general compactness theorem, assuming e.g. the ...

Logic and geometric representations constitute an interdisciplinary framework that merges formal logical systems with spatial and diagrammatic structures. This field encompasses the study of classical ...

Hallucination is fundamental to how transformer-based language models work. In fact, it's their greatest asset.

Shalosh B. Ekhad, the co-author of several papers in respected mathematics journals, has been known to prove with a single, succinct utterance theorems and identities that previously required pages of ...

When Aristotle and his predecessors devised their theories of logic and mathematics, they came up with the so-called Law of the Excluded Middle, which states that every proposition must either be true ...