BBS: Inland Empire Archive Date: 04-07-92 (01:07) Number: 179 From: MICHAEL POKRIEFKA Refer#: NONE To: JIM WELLS @ 930/21 Recvd: NO Subj: Logical operators Conf: (2) Quik_Bas

In a message of <Apr 03 18:12>, Jim Wells @ 930/21 (1:10/8) writes: BW> Could you shed some light on IMP? I see how to use BW>the others, but how isIMPused? I've never seen it used BW>(so maybe it isn't!) JW> IMP, Bill, is both a logical and arithmatic operator. Its JW> logical function returns a value of false (0) only if its first JW> operand is true and its second operand is false. JW> Here's a truth table for it: JW> x y xIMPy JW> ------------------------- JW> 1 1 1 JW> 1 0 0 JW> 0 1 1 JW> 0 0 1 JW>IMPstands for implication as in a statement is TRUE if the JW> value of the first operand implies the value of the second. A point about the logical operators as they are used in formal logic: The use of the word'implication' is regretable. (This is no slam against you,Jim, I know you're using terms is a way that has become standard. It's the standard I want to inveigh against). As far as I know, this use of the word'implication' goes back to a pioneering work on formallogic called _Principia Mathematica_ published by Alfred North Whitehead and Bertrand Russell in 1910. It invites confusion between two quite distinct notions: logical implication and (borrowing another _Principia_ usage) material implication. What Jim describes above is material implication. In formal languages developed for logic this statement connective is often written using an arrow (I'll type '-->' as an approximation). Thus, where 'A' and 'B' are '-->sentences, '(A --> B)', is read "If A then B", or, as I prefer, "A only if B". The connective'-->'has the truth table that Jim gives above. Just replace'x' with 'A', 'y' with'B', and 'xIMPy' with '(A --> B)'. Logical implication, by way of contrast, isnot a statement connective at all. It does not join two statements to make a longer statement. It joins the names of statements and asserts that a special logical relation holds between the statements named. (The usual convention for naming expressions is similar to the one used in QB programming. We enclose the expression in single quotes. Hence,'Boston' names a word,viz., the word within the quotes, whereas the word without the quotes names a city). In formal logic, logical implication is often written using a double arrow (I'll type '==>' as an approximation). A statement 'A' logically implies a statement 'B' just in case every assignment of truth to'A' also assigns truth to 'B'.There is a relationship between'-->' and '==>':'A' ==> 'B' if and only if '(A --> B)' is logically truewhere a statement is _logically true_ just in case it is assigned truth in every row of it's truth table. 'AORNOTA' is an example of a logical truth: ANOTA (AORNOT A) -------------------------- 1 0 1 0 1 1 Regards, Michael --- msgedsq 2.0.4 * Origin: Michael's Bar and Grill (1:226/70.1)

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