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Equivalently, a conditional is true if the antecedent is contained in the convex hull of the points that satisfy both the antecedent and consequent. Our result is then that every consistent formula without nested conditionals is satisfiable in a model based on a finite set of points in the plane. The proof relies on a result by Richter and Rogers showing that every finite abstract convex geometry can be represented by convex polygons in the plane.<\/jats:p>","DOI":"10.1017\/s1755020321000356","type":"journal-article","created":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T08:27:25Z","timestamp":1625732845000},"page":"529-552","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["CONDITIONAL LOGIC IS COMPLETE FOR CONVEXITY IN THE PLANE"],"prefix":"10.1017","volume":"16","author":[{"given":"JOHANNES","family":"MARTI","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,7,8]]},"reference":[{"key":"S1755020321000356_r23","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-4896(98)00044-4"},{"key":"S1755020321000356_r5","doi-asserted-by":"publisher","DOI":"10.2307\/2550390"},{"key":"S1755020321000356_r42","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/9.5.601"},{"key":"S1755020321000356_r31","doi-asserted-by":"publisher","DOI":"10.2307\/1969080"},{"key":"S1755020321000356_r12","doi-asserted-by":"publisher","DOI":"10.14232\/actasm-016-044-8"},{"key":"S1755020321000356_r9","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093883341"},{"key":"S1755020321000356_r1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7622-2"},{"key":"S1755020321000356_r21","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2004.05.001"},{"key":"S1755020321000356_r14","doi-asserted-by":"publisher","DOI":"10.1007\/BF00149365"},{"key":"S1755020321000356_r18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00247909"},{"key":"S1755020321000356_r7","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2006.05.034"},{"key":"S1755020321000356_r19","doi-asserted-by":"publisher","DOI":"10.2307\/2214372"},{"key":"S1755020321000356_r41","unstructured":"[41] Veltman, F. 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