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Logic

From Simple English Wikipedia, the free encyclopedia

Logic is the science of reasoning. Logic helps people decide whether something is true or false.

A popular example, given by Aristotle:

  1. All humans are mortal (They die at some point)
  2. Aristotle is a human
  3. Therefore, Aristotle is mortal.

\land is read like "and", meaning both of the two. \lor is read like "or", meaning at least one of the two. \Rightarrow is read like "implies", or "If ... then ...". \lnot is read like "not", or "it is not the case that ...".

This is the same example using logic symbols:

(human \Rightarrow mortal) \land (Aristotle \Rightarrow human)  \Rightarrow (Aristotle\Rightarrow mortal)

And this is the same example using general terms:

(a \Rightarrow b) \land (c \Rightarrow a) \Rightarrow (c \Rightarrow b)

Finally, those talking about logic talk about logic clauses. A clause is simply something like "Aristole is human" or "all humans are mortal". Clauses have a truth value; they are either true or false, but not both. Mistakes in logic are called "fallacies".

There are statements that are always true.

(a \lor \lnot a) is always true. It is called a tautology. (for example: "It rains, or it does not rain")

Logic is used by computers in what is called an algorithm. An algorithm is sort of like a cooking recipe; it tells the computer what to do and when to do it.

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