Higher Order Logic

Higher-order logic (HOL) is a powerful formal system extending first-order logic by allowing quantification over predicates and functions, enabling more expressive reasoning about complex systems. Current research focuses on developing robust semantics for HOL programming, particularly within the context of non-monotonic reasoning and its applications in areas like artificial intelligence and automated theorem proving. This involves exploring different model architectures, such as stable model semantics and its extensions, and leveraging proof assistants like Isabelle/HOL for formal verification and analysis of HOL-based systems. The resulting advancements enhance the capabilities of automated reasoning tools and facilitate rigorous verification in diverse fields, from program verification to the training of constrained neural networks.