RE: Review Direct Semantics

Hello,

[snip]

> >> * 2.5 Inference Problems
> >>
> >>  - Now that all inference problems are defined w.r.t. a datatype D,
> >>    we have the problem that the term "model" is not defined w.r.t. D.
> >>
> >
> > A model is an interpretation, so it is clearly defined w.r.t. D. In
> > all
> > definitions of the inference problems, we already say things such as
> > "a model
> > w.r.t. D exists".
> 
> Yes, that's the reason why I wanted to see the term "model w.r.t. D"
> defined in addition to "model" only. Since for interpretations the
> term is "interpretation *for* D", it might not be obvious to the
> reader that "model w.r.t. D" means "model that is an interpretation
> for D".
> 
> > I'm not sure whether being more explicit would be desirable: if
> > would just
> > complicate the terminology without any substantial additional
> > information.
> 
> I don't think that adding the sentence "A model of O w.r.t. D is an
> interpretation for D that is a model of O." would complicate
> terminology. It simply gives the reader a point of reference for the
> terminology already used in defining the inference problems.
> 

Fair enough -- I've changed the definition of the model to be explicit about the
datatype map. I haven't, however, changed the last sentence in Section 2.5: this
sentence is meant to be explanatory and it seems to me that adding a bunch of
"w.r.t. D" and "for D" would just make it harder to understand.

> [snip]
> >> * Throughout
> >>
> >>  - When viewing the document with sans-serif fonts, the capital
> >>    letter I and the digit 1 can hardly be distinguished. This
> >>    complicates reading some of the expressions used in the document,
> >>    e.g. those in the 3rd and 4th line of Table 4. In 2.4, you even
> >>    use I_1, which contains \Delta_I and \cdot^{I_1}, but all
> >>    subscripts read like the capital I.
> >>
> >>    I remember that Boris has mentioned this problem in the last
> >>    discussion, but I don't think we've fully discussed the
> >>    alternatives here. I'm aware that possible changes can be
> >>    far-reaching and therefore require a lot of work, but still I'd
> >>    prefer to avoid confusion whenever possible. So how about using
> >>    the capital "J" instead of "I"?
> >>
> >
> > I've changed I into J in the definition of models. (I believe the
> > latter was the
> > only place where we used {I_1}.)
> 
> Thanks, that's better.
> 
> > The changed text looks again quiet ugly, but there is nothing I can
> > do here:
> > HTML is just completely inadequate for typesetting mathematics and
> > we will just
> > have to live with this ugliness.
> 
> (1) I agree that the maths will always look ugly.
> 
> (2) But I don't think we have to live with the addressed ambiguity. My
> suggestion was actually to replace I with J *globally*, which could
> avoid confusion at least between the capital letter I and the digit 1
> used in super-/subscripts. I'm aware that this change (a) doesn't make
> the maths nicer (which just confirms theorem (1) ;-)), and (b) can
> have far-reaching consequences. But it might make reading easier,
> which I find a justifiable motivation. As for (b), I can offer help
> with the necessary changes.
> 

But now there aren't any I_1 in the document, so there is no need to change
anything and we should be fine, right? I'm not convinced that changing the
remaining Is into Js is necessary (and/or desired).

Regards,

	Boris

> Cheers
> 
> Thomas
> 
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> |  Dr Thomas Schneider                         schneider@cs.man.ac.uk  |
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Received on Monday, 6 April 2009 11:49:15 UTC