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In propositional logic, modus tollens (/ ˈ m oʊ d ə s ˈ t ɒ l ɛ n z /) (MT), also known as modus tollendo tollens (Latin for "mode that by denying denies") [2] and denying the consequent, [3] is a deductive argument form and a rule of inference. Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q ...
Modus ponendo tollens (MPT; [1] Latin: "mode that denies by affirming") [2] is a valid rule of inference for propositional logic. It is closely related to modus ponens and modus tollendo ponens . Overview
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. [1] [2] It is one of the three laws of thought, along with the law of noncontradiction, and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens ...
In statistics, the mode is the value that appears most often in a set of data values. [1] If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e., x=argmax x i P(X = x i)).
This is the modus ponens rule of propositional logic. Rules of inference are often formulated as schemata employing metavariables . [ 2 ] In the rule (schema) above, the metavariables A and B can be instantiated to any element of the universe (or sometimes, by convention, a restricted subset such as propositions ) to form an infinite set of ...
In a fuzzy rule, modus ponens is extended to generalised modus ponens:. [2] Premise: x is A* Implication: IF x is A THEN y is B Consequent: y is B* The key difference is that the premise x is A can be only partially true. As a result, the consequent y is B is also partially true.
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
Modulus is the diminutive from the Latin word modus meaning measure or manner. It, or its plural moduli, may refer to the following: Physics, engineering and computing