## 2.6. Semantic links between global constraints

For each global constraint entry of the catalogue, the slot See also provides links to other global constraints. Rather than just pointing to a set of constraints, we prefer to explicitly indicate the reason why we point to a given constraint. A link $\mathrm{𝑙𝑖𝑛𝑘}\left({C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}},{C}_{\mathrm{𝑎𝑙𝑠𝑜}}\right)$ from a constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ (i.e., the constraint associated with a catalogue entry) to another constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ (i.e., the constraint of the See also slot located in the catalogue entry of constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$) has a given semantics and this section describes the kind of semantic links that are currently used. Before introducing each semantic link and its meaning, let us first quote that some of them are related by one of the following relations:

• A link $\mathrm{𝑙𝑖𝑛𝑘}$ is symmetric if and only if $\mathrm{𝑙𝑖𝑛𝑘}\left({C}_{1},{C}_{2}\right)⇔\mathrm{𝑙𝑖𝑛𝑘}\left({C}_{2},{C}_{1}\right)$.

• A link $\mathrm{𝑙𝑖𝑛𝑘}$ is asymmetric if and only if $\mathrm{𝑙𝑖𝑛𝑘}\left({C}_{1},{C}_{2}\right)⇒¬\mathrm{𝑙𝑖𝑛𝑘}\left({C}_{2},{C}_{1}\right)$ ($¬\mathrm{𝑙𝑖𝑛𝑘}\left({C}_{2},{C}_{1}\right)$ is a shortcut for denoting that the link $\mathrm{𝑙𝑖𝑛𝑘}\left({C}_{2},{C}_{1}\right)$ does not occur in the catalogue).

• A link ${\mathrm{𝑙𝑖𝑛𝑘}}_{j}$ is the converse of a link ${\mathrm{𝑙𝑖𝑛𝑘}}_{i}$ if and only if ${\mathrm{𝑙𝑖𝑛𝑘}}_{i}\left({C}_{1},{C}_{2}\right)⇔{\mathrm{𝑙𝑖𝑛𝑘}}_{j}\left({C}_{2},{C}_{1}\right)$.

Table 2.6.0 lists each semantic link and the relation it has.All links are automatically checked with respect to their relations each time the catalogue is generated. Then one section describes the meaning of each semantic link.

##### Table 2.6.0. Available semantic links between constraints
assignment dimension added        converse: assignment dimension removed
assignment dimension removed        converse: assignment dimension added
attached to cost variant        converse: cost variant
common keyword        symmetric
comparison swapped        symmetric
cost variant        converse: attached to cost variant
generalisation        converse: specialisation
hard version        converse: soft variant
implied by        converse: implies
implies        converse: implied by
implies (if swap arguments)        symmetric
implies (items to collection)        asymmetric
negation        symmetric
part of system of constraints        converse: system of constraints
related        symmetric
related to a common problem        symmetric
root concept        converse: shift of concept
shift of concept        converse: root concept
soft variant        converse: hard version
specialisation        converse: generalisation
system of constraints        converse: part of system of constraints
used in graph description        asymmetric
used in reformulation        converse: uses in its reformulation
uses in its reformulation        converse: used in reformulation