Typing Description Logics Cheat Sheet

Ontology

To help you type the Unicode characters, I’ve included methods for major operating systems, however I work on a Linux machine, so I can only say with certainty that the Linux method works. However, I did a little searching for you MacOS and Windows users and included the recommended methods here.

  • Linux: press “ctrl” + “shift” + “u”, release and type the digits for the code after the ‘u’ character that appears, follow with a space to render the character. u2200 “space” will render ∀.
  • MacOS: press “ctrl” + “cmd” + “space” to bring up the characters popover. Then type the code: U+2200 to find ∀, which you can include by hitting “Enter”.
  • Windows: type “Alt” + “+” and then type the Unicode hexadecimal code (e.g., “2200”) followed by “Enter” to render ∀.

The Characters

Symbol Unicode LaTeX Description Example Read as
⊤ 22a4 \top ⊤ is a special concept with every individual as an instance ⊤ top
⊥ 22a5 \bot empty concept ⊥ bottom
∀ 2200 \forall universal restriction ∀r.C all r-successors are in C
∃ 2203 \exists existential restriction ∃r.C an r-successor exists in C
≡ 2261 \equiv Concept equivalence C≡D C is equivalent to D
≐ 2250 \doteq Concept definition C≐D C is defined to be equal to D
⊑ 2291 \sqsubseteq Concept inclusion C⊑D all C are D
⊓ 2293 \sqcap conjunction C⊓D C and D
⊔ 2294 \sqcup disjunction C⊔D C or D
¬ 00ac \neg negation or complement ¬C not C
⊢ 22a2 \vdash proves or syntactic consequence P⊢Q Q is derivable/provable from P
⊨ 22a8 \models satisfies Q⊨S Q satisfies all s for s in S
semantic consequence S’⊨Q’ If all s in S’ is True, Q’ must be true.
⊭ 22ad \not\models negation of ⊨
→ 2192 \rightarrow implication C→D C implies D
∘ 2218 \circ composition r∘s s composed with r
⁻ 207B ^- inversion r≡s⁻ r is equivalent to the inverse of s
: Concept assertion a : C a is a C
: Role assertion (a, b): r a is r-related to b

I made the cheat sheet using Google Drive so you can view it and print it: Description Logics Cheat Sheet. I recommend keeping a copy next to your keyboard.

Until next time, happy typing.
Paul