Table 1 \(\mathsf {RCC5}\) compositions. Given three regions, x, y and z, and two relationships \({\mathsf {R}}_1(x,y)\) and \({\mathsf {R}}_2(y,z)\), the relationship \({\mathsf {R}}_3(x,z)\) is not arbitrary. A map is consistent, if every triple of relationships is \(\mathsf {RCC5}\)–consistent.
\(\circ \) | \(\mathsf {DR}(y,z)\) | \(\mathsf {PO}(y,z)\) | \(\mathsf {PP}(y,z)\) | \(\mathsf {PPi}(y,z)\) | \(\mathsf {EQ}(y,z)\) |
|---|---|---|---|---|---|
\(\mathsf {DR}(x,y)\) | \(\mathsf {any}\) | \(\mathsf {DR, PO,PP}\) | \(\mathsf {DR, PO,PP}\) | \(\mathsf {DR}\) | \(\mathsf {DR}\) |
\(\mathsf {PO}(x,y)\) | \(\mathsf {DR, PO,PPi}\) | \(\mathsf {any}\) | \(\mathsf {PO, PP}\) | \(\mathsf {DR, PO,PPi}\) | \(\mathsf {PO}\) |
\(\mathsf {PP}(x,y)\) | \(\mathsf {DR}\) | \(\mathsf {DR, PO,PP}\) | \(\mathsf {PP}\) | \(\mathsf {any}\) | \(\mathsf {PP}\) |
\(\mathsf {PPi}(x,y)\) | \(\mathsf {DR, PO,PPi}\) | \(\mathsf {PO, PPi}\) | \(\mathsf {PO, EQ,PP,PPi}\) | \(\mathsf {PPi}\) | \(\mathsf {PPi}\) |
\(\mathsf {EQ}(x,y)\) | \(\mathsf {DR}\) | \(\mathsf {PO}\) | \(\mathsf {PP}\) | \(\mathsf {PPi}\) | \(\mathsf {EQ}\) |
