Table 17 Syntax and semantics of description logic [18]
Syntax | Description | Semantics |
|---|---|---|
C, D | Concepts or Classes | \(C^{{\mathcal {I}}},D^{{\mathcal {I}}}\subseteq \Theta\) |
R, S | Relations or Properties | \(R^{{\mathcal {I}}},S^{{\mathcal {I}}}\subseteq \Theta \times \Theta\) |
\(C\sqsubseteq D\) | Class subsumption | \(C^{{\mathcal {I}}}\subseteq D^{{\mathcal {I}}}\) |
\(R\sqsubseteq S\) | Property subsumption | \(R^{{\mathcal {I}}}\subseteq S^{{\mathcal {I}}}\) |
\(C\sqcup D\) | Union of classes | \((C\sqcup D)^{\mathcal {I}}=C^{{\mathcal {I}}}\cup D^{\mathcal {{\mathcal {I}}}}\) |
\(C \sqcap D\) | Intersection of classes | \((C \sqcap D)^{{\mathcal {I}}}=C^{{\mathcal {I}}} \cap D^{{\mathcal {I}}}\) |
\(\lnot C\) | Complement | \((\lnot C)^{\mathcal {I}}=\Theta - C^{{\mathcal {I}}}\) |
\(\exists R.C\) | Existential quantification | \({(\exists R.C)}^{\mathcal {I}}=\{a \in \Theta | \exists b, \langle a, b \rangle \in R^{\mathcal {I}} \wedge b \in C^{\mathcal {I}}\}\) |
\(\forall R.C\) | Value restriction | \({(\forall R.C)}^{\mathcal {I}}=\{a \in \Theta | \forall b, \langle a, b \rangle \in R^{\mathcal {I}} \rightarrow b \in C^{{\mathcal {I}}}\}\) |
\(\top\) | Top concept or Thing | \(\top ^{{\mathcal {I}}}=\Theta\) |
\(\bot\) | Bottom concept or Nothing | \(\bot ^{{\mathcal {I}}}=\varnothing\) |