# Typing Description Logics Cheat Sheet

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 for you.

**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 the code. “Alt +2200” will render into ∀.

## 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 |

## Print It Out

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