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In logic, a relation that holds between two propositions when they are linked as antecedent and consequent of a true conditional proposition. Logicians distinguish two main types of implication, material and strict. Proposition *p* materially implies proposition *q* if and only if the material conditional *p* ⊃ *q* (read “if *p* then *q*”) is true. A proposition of the form *p* ⊃ *q* is false whenever *p* is true and *q* is false; it is true in the other three possible cases (i.e., *p* true and *q* true; *p* false and *q* true; *p* false and *q* false). It follows that whenever *p* is false, *p* ⊃ *q* is automatically true: this is a peculiarity that makes the material conditional inadequate as an interpretation of the meaning of conditional sentences in ordinary English. On the other hand, proposition *p* strictly implies proposition *q* if and only if it is *impossible* for *p* to be true without *q* also being true (i.e., if the conjunction of *p* and not-*q* is impossible).

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Implication can refer to:

- Logic:
- Logical implication as regarded in mathematical logic.
- Material conditional as regarded in philosophical logic.

- Also, in linguistics, there are different specialized related notions:

- In mathematics functions can be implicit.
- In forensics, medical diagnosis, or scientific investigation, a hypothetical cause is implicated or indicated when a reason for the condition can be found, given that cause.
- Implicit can mean to imply indirectly, that is to not state it directly.

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Last updated on Tuesday February 19, 2008 at 02:38:58 PST (GMT -0800)

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This article is licensed under the GNU Free Documentation License.

Last updated on Tuesday February 19, 2008 at 02:38:58 PST (GMT -0800)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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