{"id":150348,"date":"2003-01-01T00:00:00","date_gmt":"2003-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/deciding-validity-in-a-spatial-logic-for-trees\/"},"modified":"2021-08-18T08:25:33","modified_gmt":"2021-08-18T15:25:33","slug":"deciding-validity-in-a-spatial-logic-for-trees-2003","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/deciding-validity-in-a-spatial-logic-for-trees-2003\/","title":{"rendered":"Deciding Validity in a Spatial Logic for Trees"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We consider a propositional spatial logic for finite trees. The logic includes A|B (tree composition), A|> B (the implication induced by composition), and 0 (the unit of composition). We show that the satisfaction and validity problems are equivalent, and decidable. The crux of the argument is devising a finite enumeration of trees to consider when deciding whether a spatial implication is satisfied. We introduce a sequent calculus for the logic, and show it to be sound and complete with respect to an interpretation in terms of satisfaction. Finally, we describe a complete proof procedure for the sequent calculus. We envisage applications in the area of logic-based type systems for semistructured data. We describe a small programming language based on this idea.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We consider a propositional spatial logic for finite trees. The logic includes A|B (tree composition), A|> B (the implication induced by composition), and 0 (the unit of composition). We show that the satisfaction and validity problems are equivalent, and decidable. The crux of the argument is devising a finite enumeration of trees to consider when [&hellip;]<\/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":[13546,13560],"msr-publication-type":[193718],"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-150348","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2003-1-18","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"MSR-TR-2002-113","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"Microsoft","msr_how_published":"","msr_notes":"A portion of this work appears in the proceedings of the ACM SIGPLAN Workshop on Types in Language Design and Implementation, New Orleans, January 18, 2003.","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":"320480","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2003\/01\/DecidingValidity.pdf","id":"320480","title":"Deciding validity in a spatial logic for trees","label_id":"243109","label":0},{"type":"file","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/tr-2002-113.pdf","id":"210397","title":"Technical Report MSR-TR-2002-113 (Extended 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