mathematical logic


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mathematical logic:

see symbolic logicsymbolic logic
or mathematical logic,
formalized system of deductive logic, employing abstract symbols for the various aspects of natural language. Symbolic logic draws on the concepts and techniques of mathematics, notably set theory, and in turn has contributed to
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.

Mathematical Logic

 

a branch of logic that makes use of mathematical methods.

The use of formal languages with an exact syntax and precise semantics that unambiguously define the meaning of formulas is characteristic of mathematical logic. The need for such a logic arose in the early 20th century in connection with the intensive development of the foundations of mathematics, the emergence of set theory in which antinomies had been discovered, the refinement of the concept of an algorithm, as well as with other profound and fundamental problems of mathematical science. The importance of mathematical logic for science as a whole, however, is not exhausted by its mathematical applications, since all sciences require good reasoning and methods of proof. This is why mathematical logic can rightfully be called logic in its most recent development.

A. A. MARKOV

mathematical logic

[¦math·ə¦mad·ə·kəl ′läj·ik]
(mathematics)
The study of mathematical theories from the viewpoint of model theory, recursive function theory, proof theory, and set theory.
References in periodicals archive ?
Since formal methods use mathematical logic for the specification of software systems, the resulting specifications are free of ambiguities, incompleteness and contradictions.
Mathematical Logic: An Application Oriented Approach.
Belohlavek, "Lattices of fixed points of fuzzy Galois connections," Mathematical Logic Quarterly, vol.
Artificial intelligence, knowledge engineering are based on the symbolic mathematical logic, discipline maximally purged of subjective emotional worlds.
The reasoning is less grounded in mathematical logic while it is much more concerned with the empirical and inductive description of specific market configurations.
Every child is not able to grasp mathematical logic due to various reasons which may hinder the mathematical learning.
Each procedure chapter reviews the mathematical logic on which the statistical test is based and the basic tools necessary for comprehending the literature published in the statistics journals.
Physics and technique can not be theories in the sense of mathematical logic. They must be interpreted by theories which are "empirically significant" (the term in quotations was often used some three or four decades ago in the philosophy of science).
It is an impossible comparison to make and, moreover, it is an argument that defies simple mathematical logic.
It is not merely a study of lay or everyday logic, but instead, of professional research in mathematical logic. There is such a wealth of empirical studies in science and technology studies (STS) that a study of logic might seem unremarkable.
Aware of the philosophical landscape at the time, Jones, in a humorous passage, offers her assessment: "Positivism has no God and no external world; logical positivism has no God and no external world but it does have mathematical logic; Kantianism has no external world but does have God; and realism allows for both God and an external world." German mathematicians and physicists, while not philosophically illiterate, did not usually demonstrate philosophical leanings, at least not on the job and for the most part did not try to bring their scientific activity into logical connection with their philosophy.
Relationship between variable parameters and the original introduced through mathematical logic relations.

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