Overview of the most important logical symbols with references to the corresponding articles.
Note: Over the history of logic, a number of different and sometimes contradictory symbol systems have been developed, many of which are still in use today. The attempt has been made to also list various alternative symbols that may be found in other publications. Among these, there are also symbols that may have confusing meanings. Those are marked with an underline to indicate that their use is discouraged.
| Symbol | Alternatives | Short name | Description | Article |
|---|---|---|---|---|
A ⟶ B | →, ⇒, ⟹, ⊃, ⊨, ≻ | if | “If A, then B“ | Conditional |
A ⟷ B | ↔, ⇔, ⟺, ≡, ~, ≻≺ | iff | „B exactly when A“ | Biconditional |
A ∧ B | &, ∩, · | and | „A and B“ | Conjunction |
A ∨ B | ∥, + | or | „A or B [or both]“ | Adjunction |
A ⊻ B | ⩒, ⊕, ≢, ↮, >< | xor | „A or B [but not both]“ | Contravalence |
¬ A | !, ‾‾, ∼ | not | „not B“ | Negation |
See also Junctor
| Symbol | Alternatives | Description | Article |
|---|---|---|---|
∀ A: B | ͓∧ | „For all A it is true, that B“ | Universal quantification |
∃ A: B | ͓∨ | „There exist [at least one] A, for which B is true“ | Existential quantification |
∄ A: B | „There exists no A, for which B is true“ | Universal quantification§Negation |
See also Quantifier
| Symbol | Alternatives | Description | Article |
|---|---|---|---|
A ≡ B | ↔, ⟷, ⇔, ⟺ | “A is logically equivalent to B” | Logical equivalence (see also Biconditional and Contravalence) |
A ≢ B | ↮, ⇎ | “A is not logically equivalent to B” |
| Symbol | Alternatives | Description | Article |
|---|---|---|---|
A ⇑ | ↑ | “A is upward entailing“ | Upward/downward entailment (see also Distribution) |
A ⇓ | ↓ | ”A is downward entailing“ „A is distributed“ |
Only those symbols which are used in articles on this site are listed here:
| Symbol | Alternatives | Description | Article |
|---|---|---|---|
∅ | {}, ⦰, Ø, 𝛷, 0 , ε, Λ | Empty set | Empty set |