{"id":335471,"date":"2016-12-12T14:43:00","date_gmt":"2016-12-12T22:43:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=335471"},"modified":"2018-10-16T20:08:40","modified_gmt":"2018-10-17T03:08:40","slug":"automatically-generating-problems-solutions-natural-deduction","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/automatically-generating-problems-solutions-natural-deduction\/","title":{"rendered":"Automatically Generating Problems and Solutions for Natural Deduction"},"content":{"rendered":"

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 <\/em>(UPG) that encodes all<\/em> possible applications of inference rules over all small<\/em> propositions abstracted using their bitvector-based truth-table representation<\/em>. 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.<\/p>\n","protected":false},"excerpt":{"rendered":"

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 […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13556,13560],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-335471","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"","msr_edition":"IJCAI '13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence","msr_affiliation":"","msr_published_date":"2013-08-03","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"1968-1975","msr_chapter":"","msr_isbn":"978-1-57735-633-2","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"335480","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"Automatically Generating Problems and Solutions for Natural Deduction","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/12\/ijcai13-pgen.pdf","id":335480,"label_id":0},{"type":"file","title":"Automatically Generating Problems and Solutions for Natural Deduction (Poster)","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/12\/ijcai13-pgen.pptx","id":335483,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":335483,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/12\/ijcai13-pgen.pptx"},{"id":335480,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/12\/ijcai13-pgen.pdf"}],"msr-author-ordering":[{"type":"text","value":"Umair Z. 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