Editing Web Ontology Language (section)

=== Logic ===
To choose a subset of first-order logic that is decidable, [[propositional logic]] was used, increasing its  power by adding logics represented by convention with acronyms:
{| class="wikitable"
!Letter or symbol of logic
!Description
|-
|<math>\mathcal{AL}</math>
|Inclusion and equivalence between classes, definition of atomic classes, universe class, intersection between classes, definitions of classes formed by elements that take part in relationships or have a relationship of a certain type only with elements of a certain class, congruence operator between individuals and an individual's membership in a class
|-
|<math>\mathcal{ALC}</math>
|adds to AL the empty class, the complement classes, the union of classes and the classes of elements that are in a certain relationship with elements of a certain class
|-
|<math>\mathcal{S}</math>
|Adds the definition of the transitivity of a relation to ALC
|-
|<math>\mathcal{H}</math>
|Inclusion and equivalence between relations
|-
|<math>\mathcal{R}</math>
|disjunction of properties, reflexivity, asymmetry, irreflexivity, relations composed of other relations, definition of non-relationship between two individuals
|-
|<math>\mathcal{O}</math> (One of)
|creation of classes via list of all and only the individuals contained
|-
|<math>\mathcal{I}</math> (Reverse)
|definition of inverse property
|-
|<math>\mathcal{F}</math> (Feature)
|definition of functional properties
|-
|<math>\mathcal{N}</math> (Number)
|cardinality restriction: number of elements participating in a certain relationship less than, greater than or equal to a value n
|-
|<math>\mathcal{Q}</math> (Qualified)
|like N, but the relationship can be qualified
|-
|<math>\mathcal{D}_n</math> (Countable domain)
|definition of domains ([[data types]]) to which a relationship can lead (e.g. "Mario is n years old")
|}