• README ⤓ .txt 2026-07-17T121634.146 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 2026-07-17T121634.146 000000000000928
  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 (1997; "Cardinal directions between extended spatial objects", IEEE TKDE) 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 2026-07-16T165328.000 000000000053168
  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 2026-07-15T060909.000 000000000022512
  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.
• Region Connection Calculus ⤓ .md 2026-07-15T211301.000 000000000014352
  Randell, Cui, Cohn (1992). Qualitative spatial reasoning. Mereotopology. RCC-8. Foundation of spatial AI.
• Spatial Logic ⤓ .md 2026-07-15T060659.000 000000000021672
  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).