Definitions for mathematical logic
math·e·mat·i·cal log·ic

Princeton's WordNetRate this definition:0.0 / 0 votes

1. symbolic logic, mathematical logic, formal logicnoun

   any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity

WiktionaryRate this definition:0.0 / 0 votes

1. mathematical logicnoun

   A subfield of logic and mathematics consisting of both the mathematical study of logic and the application of this study to other areas of mathematics, exemplified by questions on the expressive power of formal logics and the deductive power of formal proof systems.

WikipediaRate this definition:0.0 / 0 votes

1. Mathematical logic

   Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather than trying to find theories in which all of mathematics can be developed.

ChatGPTRate this definition:0.0 / 0 votes

1. mathematical logic

   Mathematical logic, also known as symbolic logic, is a subfield of mathematics that is concerned with the application of formal logic to mathematics. It involves the study of formal systems, proof theory, model theory, computability theory, set theory, and recursion theory. This branch of mathematics uses formal methods to represent logical arguments and identify logical relations and properties, examine consistency or equivalent interpretations, and establish axioms and theorems. Mathematical logic is considered foundational math and it is applied in areas like computer science, philosophy, linguistics, and artificial intelligence.

WikidataRate this definition:5.0 / 2 votes

1. Mathematical logic

   Mathematical logic is a subfield of mathematics with close connections to the foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science mathematical logic encompasses additional topics not detailed in this article; see logic in computer science for those. Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems rather than trying to find theories in which all of mathematics can be developed.

Matched Categories

1. • Logic

How to pronounce mathematical logic?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say mathematical logic in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of mathematical logic in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of mathematical logic in Pythagorean Numerology is: 8

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=mathematical logic
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Mathematical_Logic
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Mathematical_Logic
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=mathematical logic