My head boggles. This is like trying to understand game theory.
On Sun, 05 Dec 2004 11:40:38 -0500, Brian van den Broek
<[EMAIL PROTECTED]> wrote:
> Kent Johnson said unto the world upon 2004-12-05 06:55:
> > RPN reverses the order of operator and operand, it doesn't reverse the
> > whole string. So in Polish Notation 2 + 3 is +23 and (2 + 3) - 1 is
> > -+231; in RPN they become 23+ and 23+1-
> >
> > Kent
>
> Hi all,
>
> Thanks Kent, that is what I had assumed it would be by analogy to Polish
> notation in logic. Somewhere on the thread, I though it had been
> asserted that all opps and operands were separated. For a bit there, I
> thought I'd gone all goofy :-) So, thanks for clearing that up.
>
> Thanks also for the other interesting posts on the thread.
>
> Largely off-topic things follow:
>
> One other advantage, at least from the logicians perspective is that
> standard "infix" notation is only able to comfortably deal with binary
> and unary operations (operations that have 2 or 1 arguments). For
> arithmetic, where you can do everything with zero, successor,
> multiplication, and addition, that isn't so important. But notice that
> general function notation, in Python and in math, is also Polish -- to
> write a 4 placed function that takes, say, the greatest common divisor
> of two numbers, and the least common multiple of two others, and tells
> you if the first divides the second, you've got to write:
> f(a,b,c,d).
>
> So, Polish notation makes manifest the conceptual similarity between the
> addition -- ADD(a,b) -- 2-placed function and arbitrary n-placed functions.
>
> This also helps out a lot in some of the areas where formal logic and
> formal semantics for natural languages bleed into each other. At a cost
> of patience, all truth functions can be expressed in terms of the "not
> both" truth function, so polyadic truth-functions past binary don't
> really need Polish notation.
>
> But, when you consider the quantifiers ('for everything . . .' and
> 'there is at least on thing . . . '), standard ones are one-placed (with
> a given universe of discourse set assumed). In the 1950's and 1960's
> mathematicians began exploring generalizations of the quantifier notion.
> There have, since the 1980's, been a sizable group of linguists who
> argue that natural language quantification is almost always 2 or higher
> placed. After two places, this too needs Polish notation (or heroic and
> ugly conventions).
>
>
>
> Brian vdB
>
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