1. Description Logic Syntax - quoll/DLe GitHub Wiki
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 |
Most of the above notation is supported in DLe. The only exception is role value map.
❇︎ The default feature chain syntax simply concatenates properties. This won't work for general properties:
e.g.parentsiblingchildname ⊑ cousinNameInstead, the composition character
∘is also used for chains:
parent ∘ sibling ∘ child ∘ name ⊑ cousinName
‡ role value map is not supported in OWL, and is not part of DLe.†
(=𝑛 𝑟)is a DLe/OWL convenience and is not primitive syntax. OWL defines this as(≤𝑛 𝑟) ⊓ (≥𝑛 𝑟).