## Quantifier

## What is a quantifier?

**A quantifier describes a mathematical operator that determines the validity of statements.** Quantifiers, also called quantifiers, are assigned to the so-called predicate logic. Predicate logic is an extension of propositional logic. Informally, quantifiers are also called written abbreviations of spoken statements.

### Types

The most common types of quantifiers are all-quantors and existential quantifiers. Other types of quantifiers, such as number quantifiers or unique existential quantifiers, can be traced back to all-quantifiers or existential quantifiers.

**An all quantifier can be interpreted as a conjunction, i.e. as a concatenation of logical AND links.** It determines the validity of a statement form, for example A(?). ? represents a variable. The notation ∀? says "for all/every ? is valid". The all quantifier can be seen as an upside-down letter "A". The expression ∀? : ?² ≤ 0 means, for example: "for all ? it is true that ?² ≤ 0", where "for all" represents the all-quantor, ? the variable and ?² ≤ 0 the propositional form.

**In contrast to an all-quantifier, an existential quantifier can be regarded as a disjunction, i.e. as a concatenation of logical OR operations.** The expression ∃? describes "there exists at least one ?", for which the postposed statement form applies. ∃? : ?² ≤ 0 means in comparison to before: "there is at least one number ? to which the propositional form ?² ≤ 0 applies", i.e. the propositional form is true. The symbol ∃ can be seen as a horizontally mirrored letter "E".

For both all-quantifiers and existential quantifiers, the reference quantity to which the respective quantifier refers must be unambiguously defined. If it is not clear from the context, the reference quantity for all-quantors must be specified by the expression ∀? ∊ M : A(?), for existential quantifiers the expression ∃? ∊ M : A(?) can be defined. The element sign ∊ indicates that the object ∀? or ∃? is an element of a set M.

## What are quantifiers in regular expressions (regex)?

Regular expressions, or regex for short, describe character strings which are used in programming languages or in the search-and-replace function and which are assigned to the **Description of these chains by certain syntactic rules** serve. Regex can be interpreted as a general notation for describing textual patterns and are used in textual analysis, structural as well as Data analytics.

Quantifiers in regular expressions specify the truth condition for a match in the search. The **Quantors are divided into a greedy version and a non-greedy or inert version.**. While a greedy version tries to find an element as often as possible, a lazy version tries to find an element as rarely as possible. The following table shows the notation of the standard quantifiers in their greedy and lazy versions.

GreedyQuantifier | SupportQuantifier | Description |

* | *? | with zero or more occurrences. |

+ | +? | with one or more occurrences. |

? | ?? | with zero or one occurrence. |

{n} | {n}? | Conformity with exactly n Occurrence. |

{n,} | {n,}? | Compliance with at least n Occurrence. |

{n,m} | {n,m}? | Consistency with n to m Occurrence. |

In addition to the described standard expressions in Regex, there are other special forms such as lookahead and lookbehind. These are used to search for expressions that return only a (relevant) part of the searched expression and are intended for further processing.

**Lookahead**If, for example, every "a" in a text is searched for which is followed by the letter "b" and only "a" is to be returned, this can be achieved by Lookahead.

The syntax "a(?=b)" searches for the term "ab" always returns only "a" as a result.**Lookbehind**The opposite is true for lookbehind. The name lookbehind is explained by the fact that preceding characters are also included in the search.

The syntax for "(? <=a)b" also searches for the term "ab", but always returns only "b" as a result.