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2. Language of mathematics - Wikipedia

   en.wikipedia.org/wiki/Language_of_mathematics

   June 2022) (Learn how and when to remove this message) The language of mathematics or mathematical language is an extension of the natural language (for example English ) that is used in mathematics and in science for expressing results ( scientific laws , theorems , proofs , logical deductions , etc.) with concision, precision and unambiguity.

3. Formal system - Wikipedia

   en.wikipedia.org/wiki/Formal_system

   Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). Deductive system, deductive apparatus, or proof system, which has rules of inference that take axioms and infers theorems, both of which are part of the formal ...

4. Mathematical logic - Wikipedia

   en.wikipedia.org/wiki/Mathematical_logic

   Concerns that mathematics had not been built on a proper foundation led to the development of axiomatic systems for fundamental areas of mathematics such as arithmetic, analysis, and geometry. In logic, the term arithmetic refers to the theory of the natural numbers .

5. Outline of logic - Wikipedia

   en.wikipedia.org/wiki/Outline_of_logic

   Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science.Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language.

6. Formal grammar - Wikipedia

   en.wikipedia.org/wiki/Formal_grammar

   A formal grammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.

7. Logic - Wikipedia

   en.wikipedia.org/wiki/Logic

   However, it can also include attempts to use logic to analyze mathematical reasoning or to establish logic-based foundations of mathematics. [165] The latter was a major concern in early 20th-century mathematical logic, which pursued the program of logicism pioneered by philosopher-logicians such as Gottlob Frege, Alfred North Whitehead , and ...

8. English grammar - Wikipedia

   en.wikipedia.org/wiki/English_grammar

   The first published English grammar was a Pamphlet for Grammar of 1586, written by William Bullokar with the stated goal of demonstrating that English was just as rule-based as Latin. Bullokar's grammar was faithfully modeled on William Lily's Latin grammar, Rudimenta Grammatices (1534), used in English schools at that time, having been ...

9. Parsing expression grammar - Wikipedia

   en.wikipedia.org/wiki/Parsing_expression_grammar

   In computer science, a parsing expression grammar (PEG) is a type of analytic formal grammar, i.e. it describes a formal language in terms of a set of rules for recognizing strings in the language. The formalism was introduced by Bryan Ford in 2004 [ 1 ] and is closely related to the family of top-down parsing languages introduced in the early ...