Definition:Formal Language
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Definition
A formal language is a structure which contains:
- An alphabet of symbols;
- A set of words made up symbols from that alphabet;
- A formal grammar which determines which words belong to the formal language and which do not.
Alphabet
Let $\mathcal L$ be a formal language.
Then there exists a specifically-defined set of symbols from which words in $\mathcal L$ may be constructed.
That set of symbols is called the alphabet of $\mathcal L$.
An alphabet consists of the following parts:
Depending on the specific nature of any particular formal language, these too may be subcategorized.
Primitive Symbol
Let $\mathcal A$ be the alphabet of a formal language $\mathcal L$.
The symbols which comprise $\mathcal A$ are called the primitive symbols of $\mathcal A$.
It is usual, during the development of a formal system, to introduce further symbols in order to abbreviate what would otherwise be unwieldy constructions.
Hence the distinction between these newly-introduced symbols and the primitive symbols.
Sources
- E.J. Lemmon: Beginning Logic (1965): $\S 2.1$
- M. Ben-Ari: Mathematical Logic for Computer Science (1993): $\S 1.2$
- H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability (1996): $\S 1.2$
