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mathematical deduction

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  • Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …   Wikipedia

  • Deduction theorem — In mathematical logic, the deduction theorem is a metatheorem of first order logic.[1] It is a formalization of the common proof technique in which an implication A → B is proved by assuming A and then proving B from this assumption.… …   Wikipedia

  • Mathematical proof — In mathematics, a proof is a convincing demonstration (within the accepted standards of the field) that some mathematical statement is necessarily true.[1][2] Proofs are obtained from deductive reasoning, rather than from inductive or empirical… …   Wikipedia

  • Mathematical fallacy — In mathematics, certain kinds of mistakes in proof, calculation, or derivation are often exhibited, and sometimes collected, as illustrations of the concept of mathematical fallacy. The specimens of the greatest interest can be seen as… …   Wikipedia

  • Mathematical jargon — The language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in… …   Wikipedia

  • Natural deduction — In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the natural way of reasoning. This contrasts with the axiomatic systems which instead use… …   Wikipedia

  • List of mathematical logic topics — Clicking on related changes shows a list of most recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in related changes. This is a list of mathematical logic …   Wikipedia

  • Theory (mathematical logic) — This article is about theories in a formal language, as studied in mathematical logic. For other uses, see Theory (disambiguation). In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually… …   Wikipedia

  • Judgment (mathematical logic) — In mathematical logic, a judgment can be for example an assertion about occurrence of a free variable in an expression of the object language, or about provability of a proposition (either as a tautology or from a given context); but judgments… …   Wikipedia

  • Structure (mathematical logic) — In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations which are defined on it. Universal algebra studies structures that generalize the algebraic structures such as… …   Wikipedia

  • Hilbert-style deduction system — In logic, especially mathematical logic, a Hilbert style deduction system is a type of system of formal deduction attributed to Gottlob FregeMáté Ruzsa 1997:129] and David Hilbert. These deductive systems are most often studied for first order… …   Wikipedia

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