1. Description Logic Syntax

Description Logic

Description Logic (DL) provides a formal notation and set of semantics for describing data. The following table provides the names and syntax for standard DL, as listed in "Introduction to Description Logic".

Name	Syntax
Top	⊤
Bottom	⊥
Conjunction	C ⊓ D
Disjunction	C ⊔ D
Negation	¬C
Existential restriction	∃r.C
Value restriction	∀r.C
Self restriction	∃r.Self
Unqualified number restriction	(≤n r) (≥n r) (=n r)
Qualified number restriction	(≤n r.C) (≥n r.C) (=n r.C)
Nominal	{a}
Role value map	r ⊑ s
Predicate restriction	∃c1,…,ck.P
Role composition	r ∘ s
Inverse role	r⁻
Feature chain	g1⋯gnh     ❇︎
General Concept Inclusion	C ⊑ D
Concept Definition	A ≡ C
Role inclusion	r ⊑ s
Role disjointness	Disj(r,s)
Role transitivity	Trans(r)
Role functionality	Func(r)
Role reflexivity	Ref(r)
Role irreflexivity	Irref(r)
Role symmetry	Sym(r)
Role antisymmetry	Asym(r)
Concept assertion	a:C
Role assertion	(a,b):r

All of the above notation is supported in DLe.

^❇︎ The default feature chain syntax simply concatenates properties. This won't work for general properties:
e.g. parentsiblingchildname ⊑ cousinName

Instead, the composition character ∘ is also used for chains:
parent ∘ sibling ∘ child ∘ name ⊑ cousinName