Abbreviating First Order Logic With Identity and Membership
in [Logic]
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From: MoeBlee on 27 Apr 2010 11:43 On Apr 27, 10:41 am, MoeBlee <jazzm...(a)hotmail.com> wrote: > But you've not given an unambiguous machine-checkable spacing RULE. Oops, sorry, to be fair, you did just mention that you're not proposing a rigorous syntax but rather informal notational conventions. Okay, that is a different context for the discussion. Yet, still, I personally don't find your notations helpful. MoeBlee
From: MoeBlee on 27 Apr 2010 11:56 On Apr 27, 1:10 am, zuhair <zaljo...(a)gmail.com> wrote: > Regarding the set notation { : } , I think it must be maintained as it > is, but the notation { | } must be avoided, since | would be confused > for disjunction. Not really. The form for { | } can be confined to: {term | formula}. So that can't be read as {formula | formula}. MoeBlee
From: Aatu Koskensilta on 27 Apr 2010 11:57 "G. A. Edgar" <edgar(a)math.ohio-state.edu.invalid> writes: > Lots of the classic logic texts use dots instead of parentheses. And colons, and... > You get used to it after a while. Turing wrote a paper on it. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: zuhair on 27 Apr 2010 13:13 On Apr 27, 10:43 am, MoeBlee <jazzm...(a)hotmail.com> wrote: > On Apr 27, 10:41 am, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > But you've not given an unambiguous machine-checkable spacing RULE. > > Oops, sorry, to be fair, you did just mention that you're not > proposing a rigorous syntax but rather informal notational > conventions. Okay, that is a different context for the discussion. > Yet, still, I personally don't find your notations helpful. > > MoeBlee Well to me (a personal opinion) they are helpful, they definitely abbreviate writing these long formulas, in a matter that makes sense and even simplify reading these formulas, that's in addition they don't contain what I consider as clumsy notation. Regarding promoting that technique to be as what you say an: "unambiguous machine-check-able spacing RULE" I say this can be done really, but of course it will involve a lot of specifications of spacing between characters, but it is generally workable. just an "incomplete" example is to say that Rule(1):The space between any two terms and a connective between them must be equal. Rule(2):The lesser the space between a term and a connective, the first that connective be undone and vise verse, so for example P | Q>S Now the space between Q and > is lesser than that separating Q from | so we must undo "implication" before disjunction, so the above would mean: P or (Q ->S) While P|Q > S would mean (P or Q) -> S. Rule(3): spaces between a term c and two adjacent connectives (i.e. connective in which there is no intervening terms between c and these two connectives) Must be different iff the sequence of undoing the connectives makes a difference. Now suppose one wrote P|Q>S Now this notation is not acceptable, because it might make a difference to say (P or Q)->S from saying P or (Q->S), so the spaces between the variables in the above formula and the connectives must be different. However I think Rule(3) must be extended to cover up more complex formulas, in which double triple or even quadruple spacing are needed. On the other hand when the sequence of undoing connectives is immaterial then one can use equal spacing between formulas. For example we can write Q|S|P Also we can write QSP However to make a detailed algorithm governing that, in such a manner that we avoid non unique readability of all formulas, is a big job, which is something that is suitable only for computers to do, but of course it can be done. However my main interest was not that really, because if I do that I will end up with rules of spacing that are more or less as complex (or perhaps even more) as what I tried to avoid, although the net result would be more neat than these clumsy brackets. I wanted spacing to be left to the visual imaginative power of the writer, such that the writer must use spacing in such an artistic way that makes no two readers differ as to the interpretation of what he is writing. I see it as a nice short-handing of FOL formulas, and that's the main purpose behind developing them. However One thing to be mentioned here, is that although the syntax that I introduced is not an unambiguous machine-checking rule syntax, But it is meant to be written is such a way that it must avoid non unique readability, It is largely meant for Human minds to grasp it and not for machines to check it; it permits flexibility to the human mind of the writer to use his artistic capabilities to present the formulas in a non disputable manner. So the net reading of the formulas written in this way must be indisputable, although we are using a flexible syntax. Zuhair
From: zuhair on 27 Apr 2010 13:16
On Apr 27, 10:42 am, "G. A. Edgar" <ed...(a)math.ohio-state.edu.invalid> wrote: > In article > <4fbd2971-604c-4b9b-a6a6-7bae207b8...(a)q15g2000yqj.googlegroups.com>, > > zuhair <zaljo...(a)gmail.com> wrote: > > of course we can put comas as spacers between them as for example: > > > A,B|C,,|,,D,,,E > > > But this is Ugly. > > Lots of the classic logic texts use dots instead of parentheses. > You get used to it after a while. Still it is Ugly. There is no need for it, the human mind can express itself by manipulating space in a non disputable manner human minds have this flexibility to write and understand this technique even without imposing rigorous syntactical rules that are suitable for computers to avoid confusion. > > -- > G. A. Edgar http://www.math.ohio-state.edu/~edgar/ |