# A report onFormal language, Computer science and Mathematical logic    In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.

- Formal language

Early computer science was strongly influenced by the work of mathematicians such as Kurt Gödel, Alan Turing, John von Neumann, Rózsa Péter and Alonzo Church and there continues to be a useful interchange of ideas between the two fields in areas such as mathematical logic, category theory, domain theory, and algebra.

- Computer science

In mathematical logic, a formal theory is a set of sentences expressed in a formal language.

- Formal language

Formal methods are best described as the application of a fairly broad variety of theoretical computer science fundamentals, in particular logic calculi, formal languages, automata theory, and program semantics, but also type systems and algebraic data types to problems in software and hardware specification and verification.

- Computer science

These systems, though they differ in many details, share the common property of considering only expressions in a fixed formal language.

- Mathematical logic

Computer scientists often focus on concrete programming languages and feasible computability, while researchers in mathematical logic often focus on computability as a theoretical concept and on noncomputability.

- Mathematical logic ## Computability theory

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.

Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages. ## Logic

Study of correct reasoning or good arguments.

Study of correct reasoning or good arguments.   One prominent approach associates their difference with the study of arguments expressed in formal or informal languages.

Logic is studied in and applied to various fields, such as philosophy, mathematics, computer science, and linguistics.

It provides the foundation of modern mathematical logic.