Mathematical logic

Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics.

Topics in mathematical logic

The main areas of mathematical logic include model theory, proof theory

Related Topics:
Model theory - Proof theory

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and recursion theory (often now referred to as computability theory). Axiomatic set theory is sometimes considered too.

Related Topics:
Recursion theory - Computability theory - Axiomatic set theory

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There are many overlaps with computer science, since many early pioneers in computer science, such as Alan Turing, were mathematicians and logicians.

Related Topics:
Computer science - Alan Turing

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The study of programming language semantics

Related Topics:
Programming language - Semantics

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derives from model theory, as does

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program verification, in particular model checking.

Related Topics:
Program verification - Model checking

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The Curry-Howard isomorphism between proofs and programs

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relates to proof theory; intuitionistic logic and linear logic are significant here.

Related Topics:
Proof theory - Intuitionistic logic - Linear logic

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Calculi such as the lambda calculus and combinatory logic are nowadays studied mainly as idealized programming languages.

Related Topics:
Lambda calculus - Combinatory logic - Programming languages

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Computer science also contributes to logic by developing techniques for the automatic checking or even finding of proofs, such as automated theorem proving and logic programming.

Related Topics:
Automated theorem proving - Logic programming

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