{"type":"ScholarlyArticle","title":"Automatically Generating Problems and Solutions for Natural Deduction","authors":[{"name":"Umair Z. Ahmed","slug":"umair-z-ahmed","given":"Umair Z.","family":"Ahmed","affiliation":""},{"name":"Sumit Gulwani","slug":"sumit-gulwani","given":"Sumit","family":"Gulwani","affiliation":""},{"name":"Amey Karkare","slug":"amey-karkare","given":"Amey","family":"Karkare","affiliation":""}],"abstract":"Natural deduction, which is a method for establishing validity of propositional type arguments, helps develop important reasoning skills and is thus a key ingredient in a course on introductory logic. We present two core components, namely solution generation and practice problem generation, for enabling computer-aided education for this important subject domain. The key enabling technology is use of an offline-computed data-structure called Universal Proof Graph (UPG) that encodes all possible applications of inference rules over all small propositions abstracted using their bitvector-based truth-table representation. This allows an efficient forward search for solution generation. More interestingly, this allows generating fresh practice problems that have given solution characteristics by performing a backward search in UPG. We obtained around 300 natural deduction problems from various textbooks. Our solution generation procedure can solve many more problems than the traditional forward-chaining based procedure, while our problem generation procedure can efficiently generate several variants with desired characteristics.","doi":null,"url":"https://ijcai.org/proceedings/2013/291","pdf":"https://ijcai.org/proceedings/2013/0291.pdf","markdown":"https://ijcai.org/proceedings/2013/291.md","bibtex":"https://ijcai.org/proceedings/2013/bibtex/291","volume":{"slug":"2013","title":"Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2013","url":"https://ijcai.org/proceedings/2013/","year":2013,"location":"Beijing, China","dates":"3–9 August 2013","editors":"Francesca Rossi","isbn":"978-1-57735-633-2","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":291,"pages":{"first":1968,"last":1974},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}