Editing Logical framework (section)

In [[logic]], a '''logical framework''' provides a means to define (or present) a logic as a signature in a higher-order [[type theory]] in such a way that [[Provability logic|provability]] of a formula in the original logic reduces to a [[type inhabitation]] problem in the framework type theory.<ref name="Jacobs2001">{{cite book|author=Bart Jacobs|title=Categorical Logic and Type Theory|year=2001|publisher=Elsevier|isbn=978-0-444-50853-9|page=598}}</ref><ref name="Gabbay1994">{{cite book|editor=Dov M. Gabbay|title=What is a logical system?|url=https://books.google.com/books?id=XqCu4XjHrIQC&pg=PA382|year=1994|publisher=[[Clarendon Press]]|isbn=978-0-19-853859-2|page=382}}</ref> This approach has been used successfully for (interactive) [[automated theorem proving]]. The first logical framework was [[Automath]]; however, the name of the idea comes from the more widely known Edinburgh Logical Framework, '''LF'''. Several more recent proof tools like [[Isabelle (theorem prover)|Isabelle]] are based on this idea.<ref name="Jacobs2001"/> Unlike a direct embedding, the logical framework approach allows many logics to be embedded in the same type system.<ref name="BoveBarbosa2009">{{cite book|author1=Ana Bove|author2=Luis Soares Barbosa|author3=Alberto Pardo|title=Language Engineering and Rigorous Software Development: International LerNet ALFA Summer School 2008, Piriapolis, Uruguay, February 24 - March 1, 2008, Revised, Selected Papers|url=https://books.google.com/books?id=YOqHiA5MYpEC&pg=PA48|year=2009|publisher=Springer|isbn=978-3-642-03152-6|pages=48}}</ref>