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  2. Logical reasoning - Wikipedia

    en.wikipedia.org/wiki/Logical_reasoning

    In mathematics, it is used to prove mathematical theorems based on a set of premises, usually called axioms. For example, Peano arithmetic is based on a small set of axioms from which all essential properties of natural numbers can be inferred using deductive reasoning. [55] [56]

  3. Premise - Wikipedia

    en.wikipedia.org/wiki/Premise

    A premise or premiss [a] is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. [1] Arguments consist of a set of premises and a conclusion. An argument is meaningful for its conclusion only when all of its premises are true. If one or more premises are ...

  4. Inference - Wikipedia

    en.wikipedia.org/wiki/Inference

    But a valid form with true premises will always have a true conclusion. For example, consider the form of the following symbological track: All meat comes from animals. All beef is meat. Therefore, all beef comes from animals. If the premises are true, then the conclusion is necessarily true, too. Now we turn to an invalid form. All A are B ...

  5. Deductive reasoning - Wikipedia

    en.wikipedia.org/wiki/Deductive_reasoning

    An example of ampliative reasoning is the inference from the premise "every raven in a random sample of 3200 ravens is black" to the conclusion "all ravens are black": the extensive random sample makes the conclusion very likely, but it does not exclude that there are rare exceptions. [36]

  6. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. [23] [24] [25] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics.

  7. Logical consequence - Wikipedia

    en.wikipedia.org/wiki/Logical_consequence

    Consider the modal account in terms of the argument given as an example above: All frogs are green. Kermit is a frog. Therefore, Kermit is green. The conclusion is a logical consequence of the premises because we can not imagine a possible world where (a) all frogs are green; (b) Kermit is a frog; and (c) Kermit is not green.

  8. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    The following is an example of an argument within the scope of propositional logic: Premise 1: If it's raining, then it's cloudy. Premise 2: It's raining. Conclusion: It's cloudy. The logical form of this argument is known as modus ponens, [39] which is a classically valid form. [40]

  9. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T. We can see also that, with the same premise, another conclusions are valid: columns 12, 14 and 15 are T.

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