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","protected":false},"excerpt":{"rendered":"
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 […]<\/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":[193715],"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-320483","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":"Cambridge University 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