Editing HOL (proof assistant) (section)

==Underlying logic==
{{expand section|date=October 2021}}

HOL systems use variants of [[classical logic|classical]] [[higher-order logic]], which has simple axiomatic foundations with few axioms and well-understood semantics.<ref>{{cite book|last=Andrews|first=Peter B|year=2002|title=An introduction to mathematical logic and type theory: to truth through proof|edition=Second|series=Applied Logic Series|volume=27|isbn=978-1-4020-0763-7|publisher=Kluwer Academic Publishers|location=Dordrecht}}</ref>

The logic used in HOL provers is closely related to Isabelle/HOL,<ref>{{cite book|author1=Tobias Nipkow|author2=Markus Wenzel|author3-link=Lawrence C. Paulson|author3=Lawrence C. Paulson|year=2002|title=Isabelle/HOL: A Proof Assistant for Higher-Order Logic|publisher=Springer-Verlag|location=Berlin, Heidelberg|isbn=978-3-540-45949-1|author1-link=Tobias Nipkow}}</ref> the most widely used logic of [[Isabelle (proof assistant)|Isabelle]].