Logical constant
In logic, a logical constant of a language is a symbol that has the same semantic value under every interpretation of. Two important types of logical constants are logical connectives and quantifiers. The equality predicate is also treated as a logical constant in many systems of logic.
One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; that is, what special feature of certain constants makes them logical in nature?
Some symbols that are commonly treated as logical constants are:
| Symbol | Meaning in English |
| T | "true" |
| F | "false" |
| ¬ | "not" |
| ∧ | "and" |
| ∨ | "or" |
| → | "implies", "if...then" |
| ∀ | "for all" |
| ∃ | "there exists", "for some" |
| = | "equals" |
| "necessarily" | |
| "possibly" |
Many of these logical constants are sometimes denoted by alternate symbols. Defining logical constants is a major part of the work of Gottlob Frege and Bertrand Russell.