{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T07:17:51Z","timestamp":1768807071971,"version":"3.49.0"},"reference-count":21,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,2,28]],"date-time":"2013-02-28T00:00:00Z","timestamp":1362009600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Artificial Intelligence"],"published-print":{"date-parts":[[2013,2,28]]},"abstract":"<jats:p>We have shown how the nine <jats:italic>tiles<\/jats:italic> in the projection-based model for cardinal directions can be partitioned into sets based on horizontal and vertical constraints (called <jats:italic>Horizontal and Vertical Constraints Model<\/jats:italic>) in our previous papers (Kor and Bennett, 2003 and 2010). In order to come up with an expressive hybrid model for direction relations between two-dimensional single-piece regions (without holes), we integrate the well-known RCC-8 model with the above-mentioned model. From this expressive hybrid model, we derive 8 basic binary relations and 13 feasible as well as jointly exhaustive relations for the <jats:italic>x<\/jats:italic>- and <jats:italic>y<\/jats:italic>-directions, respectively. Based on these basic binary relations, we derive two separate <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mn>8<\/mml:mn><mml:mo>\u00d7<\/mml:mo><mml:mn>8<\/mml:mn><\/mml:mrow><\/mml:math> composition tables for both the expressive and weak direction relations. We introduce a formula that can be used for the computation of the composition of expressive and weak direction relations between \u201cwhole or part\u201d regions. Lastly, we also show how the expressive hybrid model can be used to make several existential inferences that are not possible for existing models.<\/jats:p>","DOI":"10.1155\/2013\/205261","type":"journal-article","created":{"date-parts":[[2013,3,1]],"date-time":"2013-03-01T12:33:26Z","timestamp":1362141206000},"page":"1-20","source":"Crossref","is-referenced-by-count":5,"title":["A Hybrid Reasoning Model for \u201cWhole and Part\u201d Cardinal Direction Relations"],"prefix":"10.1155","volume":"2013","author":[{"given":"Ah-Lian","family":"Kor","sequence":"first","affiliation":[{"name":"Arts Environment and Technology Faculty, Leeds Metropolitan University, Headingley Campus, Leeds LS6 3QS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brandon","family":"Bennett","sequence":"additional","affiliation":[{"name":"School of Computing, University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"17","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/1045-926X(92)90007-9","volume":"3","year":"1992","journal-title":"Journal of Visual Languages and Computing"},{"issue":"3","key":"18","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/02693799608902079","volume":"10","year":"1996","journal-title":"International Journal of Geographic Information Systems"},{"key":"22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/3-540-47724-1_3","volume-title":"Similarity of cardinal directions","volume":"2121","year":"2001"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1006\/jvlc.1997.0067"},{"key":"9","first-page":"315","volume":"95","year":"1997","journal-title":"Artificial Intelligence"},{"key":"19","volume-title":"Using orientation information for qualitative spatial reasoning","year":"1992"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8640.2012.00431.x"},{"issue":"3","key":"10","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1023\/A:1009712514511","volume":"1","year":"1997","journal-title":"GeoInformatica"},{"key":"31","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1006\/jvlc.1997.9999","volume":"9","year":"1998","journal-title":"Journal of Visual Languages and Computing"},{"key":"15","year":"1998"},{"key":"44","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(03)00137-1"},{"key":"34","first-page":"951","volume":"174","year":"2011","journal-title":"Artificial Intelligence"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2011.07.005"},{"key":"25","series-title":"Lecture Notes in Artificial Intelligence (LNAI)","first-page":"32","volume-title":"Reasoning mechanism for cardinal direction relations","volume":"6304","year":"2010"},{"key":"11","volume-title":"Representing and reasoning with qualitative spatial relations about regions","year":"1997"},{"issue":"3","key":"7","first-page":"204","volume":"23","year":"1981","journal-title":"Notre Dame Journal of Formal Logic"},{"issue":"1","key":"8","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1305\/ndjfl\/1093870761","volume":"26","year":"1985","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"45","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0169-023X(96)00017-1","volume":"20","year":"1996","journal-title":"Data And Knowledge Engineering"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1145\/182.358434"},{"issue":"2","key":"14","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1006\/jvlc.1994.1007","volume":"5","year":"1994","journal-title":"Journal of Visual Languages and Computing"},{"key":"32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/3-540-48384-5_12","volume-title":"Simple models for simple calculi","volume":"1661","year":"1999"}],"container-title":["Advances in Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/205261.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/205261.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/205261.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T12:04:25Z","timestamp":1607601865000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/aai\/2013\/205261\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,28]]},"references-count":21,"alternative-id":["205261","205261"],"URL":"https:\/\/doi.org\/10.1155\/2013\/205261","relation":{},"ISSN":["1687-7470","1687-7489"],"issn-type":[{"value":"1687-7470","type":"print"},{"value":"1687-7489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,28]]}}}