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Mathematical logic - Topics in mathematical logic | | Mathematical logic - Topics in mathematical logic: Encyclopedia II - Mathematical logic - Topics in mathematical logic | | The main areas of mathematical logic include model theory, proof theory and recursion theory (often now referred to as computability theory). Axiomatic set theory is sometimes considered too. There are many overlaps with computer science, since many early pioneers in computer science, such as Alan Turing, were mathematicians and logicians.
The study of programming language semantics derives from model ...
See also:Mathematical logic, Mathematical logic - History, Mathematical logic - Topics in mathematical logic, Mathematical logic - Some fundamental results, Mathematical logic - Technical reference, Mathematical logic - First-order languages and structures, Mathematical logic - Terms formulas and sentences, Mathematical logic - Assignment functions, Mathematical logic - Logical satisfaction, Mathematical logic - Logical implication and truth, Mathematical logic - Variable substitution, Mathematical logic - Substitutability | | | Mathematical logic, Mathematical logic - Assignment functions, Mathematical logic - First-order languages and structures, Mathematical logic - History, Mathematical logic - Logical implication and truth, Mathematical logic - Logical satisfaction, Mathematical logic - Some fundamental results, Mathematical logic - Substitutability, Mathematical logic - Technical reference, Mathematical logic - Terms formulas and sentences, Mathematical logic - Topics in mathematical logic, Mathematical logic - Variable substitution, Logic, Model theory, Computability logic, Game semantics, Provability logic, Interpretability logic, Sequent calculus, Intuitionistic logic, Predicate logic, Theory of institutions, Table of mathematical symbols, Infinitary logic | | |
| | | Mathematical logic: Encyclopedia II - Mathematical logic - Topics in mathematical logic
Mathematical logic - Topics in mathematical logic
The main areas of mathematical logic include model theory, proof theory and recursion theory (often now referred to as computability theory). Axiomatic set theory is sometimes considered too. There are many overlaps with computer science, since many early pioneers in computer science, such as Alan Turing, were mathematicians and logicians.
The study of programming language semantics derives from model theory, as does program verification, in particular model checking.
The Curry-Howard isomorphism between proofs and programs relates to proof theory; intuitionistic logic and linear logic are significant here. Calculi such as the lambda calculus and combinatory logic are nowadays studied mainly as idealized programming languages.
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.
Other related archivesAlan Turing, Alfred North Whitehead, Aristotle, Augustus De Morgan, Axiomatic set theory, Begriffsschrift, Bertrand Russell, Charles Peirce, Computability logic, Curry-Howard isomorphism, Cut-elimination, Game semantics, George Boole, Giuseppe Peano, Gottlob Frege, Gödel's completeness theorem, Gödel's incompleteness theorem, Infinitary logic, Interpretability logic, Intuitionistic logic, Kurt Gödel, Lambert, Leibniz, Logic, Löwenheim-Skolem theorem, Mathematical logic, Model theory, On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Paul Cohen, Predicate logic, Principia Mathematica, Provability logic, Sequent calculus, Table of mathematical symbols, Theory of institutions, abstract algebra, automated theorem proving, combinatory logic, compiler, computation, computer science, continuum hypothesis, first-order, first-order theorem provers, formal language, formal systems, foundations of mathematics, fundamental concepts of mathematics, independence, intuitionistic logic, lambda calculus, linear logic, list of topics in logic, logic, logic programming, mathematics, metamathematics, model checking, model theory, philosophical logic, philosophy of mathematics, program verification, programming language, programming languages, proof, proof theory, quantitative, recursion theory, recursively enumerable, second-order, semantics, sequent calculus
 Adapted from the Wikipedia article "Topics in mathematical logic", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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