• README ⤓ .txt 2026-10-22T165042.936 000000000000776
  Logics and calculi whose intended models are regions, points, and their spatial relations: containment, connection, contact, boundary, and distance. The domain shapes the apparatus in a specific way—the relations are qualitative rather than metric, because the reasoning these systems support is about how regions stand to one another and not about where they are.
• Cardinal Direction Calculi ⤓ .md 2026-10-22T090631.000 000000000072136
  Frank ("Qualitative spatial reasoning about cardinal directions", 1991) gave the two point-based schemes — cone-based and projection-based — that everything since has been a correction of. Ligozat, "Reasoning about cardinal directions" (Journal of Visual Languages and Computing 9, 1998), supplied the algebraic treatment of the projection-based case. Goyal and Egenhofer ("The direction-relation matrix", 1997; the journal version "Cardinal directions between extended spatial objects" was long cited as in press at IEEE TKDE but never appeared) replaced points with regions and produced the Cardinal Direction Calculus, the model the field now means by the name. Skiadopoulos and Koubarakis ("Composing cardinal direction relations", Artificial Intelligence 152, 2004) found that Goyal and Egenhofer's composition method fails on some inputs and gave a correct one; Liu, Zhang, Li, and Ying (AIJ 174, 2010) settled the complexity.
• Elementary Geometry ⤓ .md 2026-10-22T165042.936 000000000000872
  Tarski lectured on the system at Warsaw in 1926–27; publication was delayed, first by other projects and then by the war, which destroyed the galley proofs. The axioms appeared in 1948, and a reduced set in "What is elementary geometry?" (in Henkin, Suppes, and Tarski, eds., The Axiomatic Method, 1959). Gupta's Berkeley thesis (1965) removed redundancies; the definitive treatment is Schwabhäuser, Szmielew, and Tarski, Metamathematische Methoden in der Geometrie (1983). Tarski and Givant, "Tarski's system of geometry" (BSL 5, 1999), give the history.
• Mereotopology ⤓ .md 2026-08-20T092458.000 000000000034424
  Whitehead proposed region-based theories (1920s). Clarke formalized connection (1981). Combines mereology (parts) with topology (connection). Randell, Cui, Cohn: Region Connection Calculus (1992). Foundation for qualitative spatial reasoning without points.
• Nine-Intersection Model ⤓ .md 2026-10-22T180154.561 000000000000904
  Max Egenhofer and Robert Franzosa, "Point-set topological spatial relations" (International Journal of Geographical Information Systems 5(2), 1991), defined binary topological relations by the four intersections of two regions' interiors and boundaries; Egenhofer and John Herring, "Categorizing binary topological relations between regions, lines, and points in geographic databases" (technical report, University of Maine, 1991 — circulated from 1990 and cited inconsistently ever since), added the exteriors, giving the 9-intersection. Eliseo Clementini, Paolino Di Felice, and Peter van Oosterom ("A small set of formal topological relationships suitable for end-user interaction", SSD 1993) recorded the dimension of each intersection, and the resulting DE-9IM became the OGC and ISO standard predicate model. Egenhofer and Khaled Al-Taha ("Reasoning about gradual changes of topological relationships", 1992) built the conceptual neighborhood graph; Egenhofer ("Deriving the composition of binary topological relations", Journal of Visual Languages and Computing 5(2), 1994) derived the composition table.
• Region Connection Calculus ⤓ .md 2026-10-22T085530.000 000000000059336
  Randell, Cui and Cohn (1992) built a spatial logic on a single primitive, connection, following Clarke's (1981) calculus of individuals and behind it Whitehead's proposal that regions rather than points be the basic spatial entities. From C alone the mereological and topological vocabulary is defined, and the eight jointly exhaustive and pairwise disjoint relations that result — RCC-8 — became the standard constraint language of qualitative spatial reasoning. The coarser RCC-5, which drops the tangential distinction, came from the same work.
• Spatial Logic ⤓ .md 2026-08-20T102427.000 000000000037264
  Multiple traditions: topology-based (McKinsey-Tarski, 1940s), mereotopology (Whitehead, Clarke), region-based (Randell et al., 1992). Logics for spatial reasoning. Modal interpretations on topological spaces. Region Connection Calculus (RCC) for qualitative spatial relations. Applications in GIS, robotics, image analysis.
• CRITERIA ⤓ .txt 2026-07-15T232047.000 000000000011232
  Not sufficient: A topological semantics deployed to interpret a non-spatial modality (that belongs in Modal—the topology is apparatus there, not subject). A temporal interval calculus (Modal/Temporal), even though the relation algebra is the same shape. Mereology as a bare theory of parthood without a spatial or topological primitive (Theories).