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\documentclass[oneside,12pt]{article}
\begin{document}


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Referee report about the paper ``Possible-translation semantics from a
categorical point of view'', by P.\ Arndt, H.L.\ Mariano and D.C.\
Pinto

\bigskip


I found the paper very interesting, very well written, and, above all,
it is excellent as an introduction to PTSs for people who know
Category Theory but who knew very little about PTSs --- like me.

\medskip

Here are some stylistical suggestions: 1) give early in the paper
short, symbolic names to the categories of logics and strict
translations/morphisms, to the category of logics and flexible
translations/morphisms, etc; 2) use these names in many places to
remind the reader what is the category being discussed; 3) indicate
that the Definition 2.10 is now the second place in which several
categories are being named and defined; 4) in the Proposition 2.14
clarify that the coproducts like $p \coprod l$ can be built using the
construction in p.6.

\medskip

Here are the typos that I found:

\medskip


p.3: ''tensor $\to$ ``tensor

p.5: strict translations while $\to$ strict translations, while

p.6: useful -for $\to$ useful---for our purposes

p.6: Let Indeed $\to$ Let indeed

p.17: ''canonical $\to$ ``canonical

p.19: If non $\to$ If none

p.21: This will object $\to$ This will be object

\bigskip

I don't know enough about the literature on PTSs to judge the
relevance of the results in the paper, but even if they are not
especially relevant the paper in excellent in many other aspects,
including as an expository paper. I strongly recommend that it be
accepted.




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