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 ...

God is by definition a perfect being. It is more perfect to exist than to not exist. Therefore, God exists. Just given these simple ideas, a few axioms, and a fondness for pushing around abstract ...

Daniele Mundici, A Constructive Proof of McNaughton's Theorem in Infinite-Valued Logic, The Journal of Symbolic Logic, Vol. 59, No. 2 (Jun., 1994), pp. 596-602 ...

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 ...

The use of computers means that modern mathematical proofs can run to millions of pages. Such proofs can never be fully verified by humans alone. Does this mean, as some argue, the death of proof? The ...