Wikipedia
Quasi-quotation or Quine quotation is a linguistic device in formal languages that facilitates rigorous and terse formulation of general rules about linguistic expressions while properly observing the use–mention distinction. It was introduced by the philosopher and logician Willard van Orman Quine in his book Mathematical Logic, originally published in 1940. Put simply, quasi-quotation enables one to introduce symbols that stand for a linguistic expression in a given instance and are used as that linguistic expression in a different instance.
For example, one can use quasi-quotation to illustrate an instance of substitutional quantification, like the following:
"Snow is white" is true if and only if snow is white. Therefore, there is some sequence of symbols that makes the following sentence true when every instance of φ is replaced by that sequence of symbols: "φ" is true if and only if φ.Quasi-quotation is used to indicate (usually in more complex formulas) that the φ and "φ" in this sentence are related things, that one is the iteration of the other in a metalanguage. Quine introduced quasiquotes because he wished to avoid the use of variables, and work only with closed sentences (expressions not containing any variables). However, he still needed to be able to talk about sentences with arbitrary predicates in them, and thus, the quasiquotes provided the mechanism to make such statements. Quine had hoped that, by avoiding variables and schemata, he would minimize confusion for the readers, as well as staying closer to the language that mathematicians actually use.
Quasi-quotation is sometimes denoted using the symbols ⌜ and ⌝ (unicode U+231C, U+231D), or double square brackets, ⟦ ⟧, ("Oxford brackets") instead of ordinary quotation marks.