Re: how to write good CS paper

In article <Pine.SOL.4.05.10105241539290.26490-100000_at_bacon.math.uwaterloo.ca>, Jim Nastos says...
>
>On Thu, 24 May 2001, mikito Harakiri wrote:
>
>> > 2. NOTATIONS
>> > Finite Structures and Logics. All structures are assumed to be finite.
>> > A relational signature 'sigma' is a set of relation symbols
>> > {R_1 , ..., R_l}, with associated arities p_i > 0.
>
> This is a very standard notation, if one wants to talk about a bunch of
>relations.

Standard, agreed, but still awkward.

>> them within a set. I object! Those indexes would stick to the rest of the paper
>> and every orthogonal enumeration, a need for which is discovered later in the
>> game, would have to be added on top of it. If the results of the paper don't
>> depend on join operations why not to use a single relation 'A' (or universal
>> relation?). Now, if joining is coming somewhere into the picture, then why not
>
> They would index them probably so that they can make the statements they
>want to make in as much generality as possible. This is often very
>desirable.

This kind of generality is often self evident even if you don't use such notation. I'm a minority here, of course, but I'm personally uncomfortable with more than one index when those indexes enumerate different things. For example, if one index iterates through relationships, and the other one goes though arguments -- then, I have to always remember which one is which.

>> Next comes enumeration of attributes within a relation. Advocates of excessive
>> mathematical notation, again, would write something like P_i(a_1, ..., a_k)
>> (keeping index from previois part, remember?-). Now, what advantages enumerating
>> columns like this are? Are we going to use induction on the number of columns,
>> or leverage ariphmetic properties of the subscript indexes somehow? Wouldn't
>
> Advantages are plentiful. For example, if I want to make a statement
>that says for these variables a,b,c or whatever, there is *some* relation
>such that... I could say "There exists a 'j' such that a_j on the
>variables a,b,c.. whatever... has this certain property." THe indices
>allow us to pick out a relation if we choose.

In your example j is just a bind variable. My point is that using natural number for it is not very clever idea. I would write

/E R | ...
(exists R such that ...)

instead.

> You also say "keeping index from previous part, remember?" Note that
>this is NOT the same indexing, since the first one went from 1..l and this
>one goes from 1..k . This means that these two sets can be different
>sizes, probably independent of each other, and even possibly equalto each
>other if k=l. These indexes also put the emphasis that such a k and l
>exist, that is, that these sets are finite.

It would be quite surprising to know if anybody explored possibility of l=k, otherwhise it's just a peculiar artifact of the notation chosen.

Question. Is it easy to tell if all arguments are assumed belonging to the same domain in this notation? I hope you'll help me with the right answer, but both answers seem unsatisfactory:
1. If all arguments are from the same domain, then its probably a convenience to simplify a model and notation itself. It could be repaired with sets of sets and subscripts of subscripts, of course.
2. If not, then the mapping between indexes and arguments is not quite natural. It totally misses the fact that some arguments are defined on isomorphic domains.

> All these little peculiarities are a standard notation in which
>paper-readers (and even writers) have to get used to so that when
>something is writtenm, ambiguity is avoided, as is incoherence.
> The mathematical notations are used for the sake of clarity and
>precision, not to complicate things.

Let me put it another way: there is no subscripts in SQL, and one reason for it is that probably because subscripts simply are not the best set notation. Received on Sun Jul 22 2001 - 01:26:05 CEST