Скачать или смотреть Higher-Order Logic: The Code That Powers Thought

The source introduces higher-order logic (HOL), explaining its enhanced expressive power compared to traditional first-order logic. While first-order logic can only quantify individual objects, HOL extends this capability to properties of objects and even properties of properties, allowing for more abstract concepts like finitude to be expressed. It highlights monadic second-order logic (MSO) as a practical subset of HOL, particularly useful in computer science for formal verification and translating logical statements into algorithms. The source concludes by showcasing HOL's diverse applications, ranging from proving software security in critical systems to analyzing philosophical arguments for the existence of God, while also acknowledging the trade-offs of its power, such as incompleteness and philosophical questions regarding ontological commitment.