# Logical constant

In logic, a logical constant of a language ${\mathcal {L}}$ is a symbol that has the same semantic value under every interpretation of ${\mathcal {L}}$ . 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.

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?[full citation needed]

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"
$\Box$ "necessarily"
$\Diamond$ "possibly"

Many of these logical constants are sometimes denoted by alternate symbols (e.g., the use of the symbol "&" rather than "∧" to denote the logical and). Defining logical constants is a major part of the work of Gottlob Frege and Bertrand Russell.