Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger. It ...

Does God really exist? This is a question that has stirred the human heart for centuries, crossing cultures, philosophies, and faiths. In today’s world, the debate is as alive as ever, with science, ...

We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of ...

Justification logic extends traditional modal frameworks by introducing explicit representations of evidential support, thereby refining our understanding of epistemic reasoning. In contrast to ...

WHEN the brilliant French mathematician Henri Poincaré was not actually doing maths, he liked to think about the nature of mathematical creativity. Logic, he felt, was important, but it was not enough ...

DeepMind is pushing artificial intelligence into one of the hardest arenas in science, building a system that can navigate ...