Re: An instance of Russell's paradox?

Ms Knox wrote:
> >> >Ms Knox, may I also ask you to kindly make some remarks regarding the
> >> >other two questions I posted, namely, the question suggesting the
> >> >infinite generalization of the arity of every predicate (I got this
> >> >idea from Quine, but I lost trace of the actual source),
> >>
> >> Sorry, that's something I'm neither knowledgeable about nor interested
> >> in. Do you recall what benefit(s) there might be in making this
> >> extension?
> >
> >I expected that would be uniformity. But, well, I am not a
> >professional, hence my confused queries.
> >
> >> ISTM that giving up finite expressions would be giving up a
> >> lot.
> >
> >Your argument truly does sound most rational. But the uniformity case
> >seems rational too. I just wish I recalled the passage from Quine where
> >he makes a mention of it. As far as I remember, he put quite a lot of
> >stress on this.
> >
> >> >as well as the
> >> >question pertaining to the actual difference between an atom and a
> >> >predicate in philosopher(socrates) transformed into [philosopher,
> >> >socrates], where the predicate is(?) really the first atom of the
> >> >analogous list form of a proposition (the problem is, I really see no
> >> >difference whatsoever).
> >>
> >> Firstly, there is a difference. In Prolog, the [a b c] representation
> >> of lists is actually syntactic sugar for the binary (and nullary) term
> >> ".":
> >> .(a, .(b, .(c, .())))
> >>
> >> Similarly, in Lisp the (a b c) representation of lists is sugar for
> >> (a . (b . (c . NIL))))
> >
> >Yes.
> >
> >> Secondly, in Prolog the =.. predicate converts between an arbitrary term
> >> such as philosopher(socrates) and the prefix list representation of it.
> >
> >Yes.
> >
> >> These are *not* interchangeable.
> >
> >No, they are not.
> >
> >> Internally to a Prolog implementation
> >> terms may indeed be represented as some sort of list, but that is wholly
> >> different from the *external* representation of Prolog "[...]" lists
> >> using '.' terms.
> >
> >I am aware of these facts. Thank you very much, Ms Knox.
> >
> >Please, kindly let me rephrase my question. Listed below are the three
> >alternative Prolog notations for the same term: the dot (internal)
> >notation, the list notation, and the operator notation.
>

: But as I said, they are *not* the same term. The first and second
are,
: but the third is not a list term. Note that if every term were equal
to
: its list-representation term then you would immediately have infinite

: terms:
:
: [a] = .(a, .()) = [., a, [.]] = .(., .(a, .(., .()), .()))
: = [., [., a, [., ., [.]] [.]] [.]] = etc. etc.

I see. I am pretty confused as the tutorial below, says in Chapter 12
(Operators):

http://www.amzi.com/AdventureInProlog/advfrtop.htm

"We have seen that the form of a Prolog data structure is
functor(arg1,arg2,...,argN). This is the ONLY data structure in Prolog.
However, Prolog allows for other ways to syntactically represent the
same data structure. These other representations are sometimes called
syntactic sugaring. The equivalence between list syntax and the dot (.)
functor is one example. Operator syntax is another."

Nevertheless, I MAY be mistaking things. May I assure you, Ms Knox,
that I will be most happy to follow your guidenance.

(Would you, please, kindly reflect on my argument pertaining to the
advantage of uniformity in interpreting all predicates as having
infinite arity?)

> >In the context
> >of the operator notation we would call "a" - a predicate, and in the
> >other two contexts - an atom (or, better, the first atom on the list).
> >My question is, since these are merely different ways of representing
> >the same algebraic structure, are predicates really atoms (I mean, is
> >it nothing but a terminological convention to call "a" [an atom] in the
> >context of the list and dot notation, whereas [a predicate] in the
> >context of the operator notation)?
> >
> >.(a, .(b, .(c, .())))
> >[a b c]
> >a(b, c)

Thank you very much for your time.
Tom

> --
> ---------------------------
> | BBB b \ Barbara at LivingHistory stop co stop uk
> | B B aa rrr b |
> | BBB a a r bbb | Quidquid latine dictum sit,
> | B B a a r b b | altum viditur.
> | BBB aa a r bbb |
> -----------------------------

.

Relevant Pages

  • Re: An instance of Russells paradox?
    ... >>infinite generalization of the arity of every predicate (I got this ... the representation ... > of lists is actually syntactic sugar for the binary term ... notation, the list notation, and the operator notation. ...
    (sci.logic)
  • Re: Complex Subset Computing in Prolog
    ...    variables is unknown build something like distinct. ... There is often confusion when lists and sets are used (in Prolog or ... but let's do this for Prolog) and this pops up ... list representation that is not unique. ...
    (comp.lang.prolog)
  • Re: Complex Subset Computing in Prolog
    ... There is often confusion when lists and sets are used (in Prolog or ... but let's do this for Prolog) and this pops up ... almost always when the subset predicate raises its head. ... list representation that is not unique. ...
    (comp.lang.prolog)
  • Re: Complex Subset Computing in Prolog
    ...    variables is unknown build something like distinct. ... There is often confusion when lists and sets are used (in Prolog or ... but let's do this for Prolog) and this pops up ... list representation that is not unique. ...
    (comp.lang.prolog)
  • Re: Hilbert-Style proof in propositional calculus
    ... The topic lends itself to Prolog. ... about the representation of formulas as Prolog terms and ... We can then implement a Prolog predicate which succeeds ... Now let's briefly discuss representing proofs as lists ...
    (comp.lang.prolog)