Logical constant

In logic, a logical constant of a language ${\displaystyle {\mathcal {L}}}$ is a symbol that has the same semantic value under every interpretation of ${\displaystyle {\mathcal {L}}}$. 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?[1]

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"
${\displaystyle \Box }$	"necessarily"
${\displaystyle \Diamond }$	"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.