Logical constant
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In symbolic logic, a logical constant of a language L is a symbol that has the same semantic value in all models of (the expressions of) L. Two important types of logical constants are logical connectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant in many systems of logic.
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" |
| ☐ | "necessary" |
| ♢ | "possible" |
For many logical constants also other symbols are commonly used to denote them, such as the symbol "&" for logical and.
One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; that is, what special feature of certain constants that makes them logical in nature?[citation needed]
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