# Logical constant

(Redirected from Logical constants)

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][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"
${\displaystyle \Box }$ "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).

1. ^ Carnap