Date: Tue, 7 Apr 2015 18:02:33 -0700 (PDT)
From: guskant <gusni.kantu@gmail.com>
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Subject: [bpfk] Re: FA as a TAG (Was: One cannot refer to inner nodes in
 Lojban PEG)
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la xorxes has already replied while I am preparing my response, but this=20
may make the problem clearer.

I may agree the point of your idea, but have some objections.


Le mercredi 8 avril 2015 06:52:23 UTC+9, Jacob Errington a =C3=A9crit :
>
> I'm making a separate thread out of this because I'm going on a tangent=
=20
> here.
>
> On 7 April 2015 at 15:04, <co...@ccil.org <javascript:>> wrote:
>
>> Terms can have FA or tags equally well, but we don't want to merge
>> FA with BAI generally, to avoid things like "se fa" and ".i fa bo",
>> which are nonsense.
>
>
> I agree that {se fa} has no clear interpretation upon first examination.=
=20
> However, {.i fa bo} can be interpreted like any other {.i TAG bo} constru=
ct.
>
> .i broda .i TAG bo brode -> .i broda TAG lo su'u brode
>
> Hence,
> .i broda .i fa bo brode -> .i broda fa lo su'u brode
>
> This provides us with another way to do essentially what {la'e di'e} does=
.=20
> For instance,
>
> .i mi pu pensi la'e di'e .i lo mi bruna cu cmalu mutce -> .i mi pu pensi=
=20
> .ifebo lo mi bruna cu cmalu mutce
> I was thinking about this: my brother is very short.
>
> Taking this idea to the extreme, we can conceive of a somewhat silly=20
> higher-order predicate -- call it {brodrfV} for now -- whose x1 is an=20
> arbitrary sumti and whose x2 is a nullary predicate supplied with than fV=
=20
> having the value of the x1. We can define {brodrfV} with the following=20
> statement.
>
> .i ko'a brodrfV lo du'u broda <=3D> broda fV ko'a
>
>

Your idea seems not a kind of higher-order logic, but simply extraction of=
=20
an argument from a bridi. Higher-order logic deals with both predicates and=
=20
arguments in its universe of discourse, while your idea does not seem=20
requiring a universe of discourse in the clause composing x2 of {brodrfV}.

Therefore, {du'u} should be replaced with {ka}, because a bridi in=20
{du'u}-clause has a truth value based on its own universe of discourse,=20
which is generally distinguished from the universe of discourse of the=20
outer bridi. On the other hand, a bridi in {ka}-clause is an open sentence=
=20
with a free variable {ce'u}. A bridi in {si'o}-clause is also an open=20
sentence with all variables are free, but not suitable for the current=20
topic in which only one argument is extracted by {brodrfV}.

The definition should be then :

.i ko'a brodrfV lo ka fV ce'u broda <=3D> broda fV ko'a


=20

> We can derive some obvious results from this statement.
>
> .i lo brodrfV be lo du'u fV ko'a broda =3D=3D=3D ko'a
> .i fV ko'a broda =3D=3D=3D .i fi'o brodrfV ko'a broda
>
>

Based on the same idea, the first line should be :

.i lo brodrfV be lo ka fV ce'u broda =3D ko'a

which denotes a substitution of a constant satisfying x1 of {brodrfV} by=20
{ko'a}, not a result derived from the definition of {brodrfV}.

mu'o

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<div dir=3D"ltr"><div>la xorxes has already replied while I am preparing my=
 response, but this may make the problem clearer.</div><div><br></div><div>=
I may agree the point of your idea, but have some objections.</div><div><br=
></div><br>Le mercredi 8 avril 2015 06:52:23 UTC+9, Jacob Errington a =C3=
=A9crit&nbsp;:<blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-l=
eft: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"=
>I'm making a separate thread out of this because I'm going on a tangent he=
re.<br><div><br>On 7 April 2015 at 15:04,  <span dir=3D"ltr">&lt;<a href=3D=
"javascript:" target=3D"_blank" gdf-obfuscated-mailto=3D"e-kI31Gbg5oJ" rel=
=3D"nofollow" onmousedown=3D"this.href=3D'javascript:';return true;" onclic=
k=3D"this.href=3D'javascript:';return true;">co...@ccil.org</a>&gt;</span> =
wrote:<br><div><div class=3D"gmail_quote"><blockquote class=3D"gmail_quote"=
 style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Te=
rms can have FA or tags equally well, but we don't want to merge<br>
FA with BAI generally, to avoid things like "se fa" and ".i fa bo",<br>
which are nonsense.</blockquote><div><br></div><div>I agree that {se fa} ha=
s no clear interpretation upon first examination. However, {.i fa bo} can b=
e interpreted like any other {.i TAG bo} construct.<br><br></div><div>.i br=
oda .i TAG bo brode -&gt; .i broda TAG lo su'u brode<br></div><div><br>Henc=
e,<br></div><div>.i broda .i fa bo brode -&gt; .i broda fa lo su'u brode<br=
><br></div><div>This provides us with another way to do essentially what {l=
a'e di'e} does. For instance,<br><br></div><div>.i mi pu pensi la'e di'e .i=
 lo mi bruna cu cmalu mutce -&gt; .i mi pu pensi .ifebo lo mi bruna cu cmal=
u mutce<br></div><div>I was thinking about this: my brother is very short.<=
br><br></div><div>Taking this idea to the extreme, we can conceive of a som=
ewhat silly higher-order predicate -- call it {brodrfV} for now -- whose x1=
 is an arbitrary sumti and whose x2 is a nullary predicate supplied with th=
an fV having the value of the x1. We can define {brodrfV} with the followin=
g statement.<br><br></div><div>.i ko'a brodrfV lo du'u broda &lt;=3D&gt; br=
oda fV ko'a<br><br></div></div></div></div></div></blockquote><div><br></di=
v><div><br></div><div>Your idea seems not a kind of higher-order logic, but=
 simply extraction of an argument from a bridi. Higher-order logic deals wi=
th both predicates and arguments in its universe of discourse, while your i=
dea does not seem requiring a universe of discourse in the clause composing=
 x2 of {brodrfV}.</div><div><br></div><div>Therefore, {du'u} should be repl=
aced with {ka}, because a bridi in {du'u}-clause has a truth value based on=
 its own universe of discourse, which is generally distinguished from the u=
niverse of discourse of the outer bridi. On the other hand, a bridi in {ka}=
-clause is an open sentence with a free variable {ce'u}. A bridi in {si'o}-=
clause is also an open sentence with all variables are free, but not suitab=
le for the current topic in which only one argument is extracted by {brodrf=
V}.</div><div><br></div><div>The definition should be then :</div><div><br>=
</div><div>.i ko'a brodrfV lo ka fV ce'u broda &lt;=3D&gt; broda fV ko'a</d=
iv><div><br></div><div><br></div><div>&nbsp;</div><blockquote class=3D"gmai=
l_quote" style=3D"margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;=
padding-left: 1ex;"><div dir=3D"ltr"><div><div><div class=3D"gmail_quote"><=
div></div><div>We can derive some obvious results from this statement.<br><=
br></div><div>.i lo brodrfV be lo du'u fV ko'a broda =3D=3D=3D ko'a<br></di=
v><div>.i fV ko'a broda =3D=3D=3D .i fi'o brodrfV ko'a broda<br></div><div>=
<br></div></div></div></div></div></blockquote><div><br></div><div><br></di=
v><div>Based on the same idea, the first line should be :</div><div><br></d=
iv><div>.i lo brodrfV be lo ka fV ce'u broda =3D ko'a</div><div><br></div><=
div>which denotes a substitution of a constant satisfying x1 of {brodrfV} b=
y {ko'a}, not a result derived from the definition of {brodrfV}.</div><div>=
<br></div><div>mu'o</div><div><br></div></div>

<p></p>

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