Date: Sat, 16 Aug 2014 13:55:37 -0700 (PDT)
From: TR NS <transfire@gmail.com>
To: lojban@googlegroups.com
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Subject: [lojban] Re: A recursively-defined predicate for building chains
 (was: Lojban for great-great-grandfather)
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On Saturday, August 16, 2014 11:33:00 AM UTC-4, tsani wrote:
>
> Our motivation is the following: we want a predicate that takes two 
> arbitrary sumti of the same type, a binary predicate, and a number, to 
> construct a chain of applications of that predicate along intermediate 
> values to "connect" the two sumti. This is the nature of constructs such as 
> "great-great-grandfather" and "three days from now" and "the friend of a 
> friend of a friend of mine", which as we have seen through usage, are 
> difficult to concisely express. However, the underlying principle of all 
> the words is the same.
>
> We propose a predicate to construct such chains, of arbitrary length, 
> defined as follows in Lojban:
>
> .i lo ka broda cu ka ko'a ko'e fo'a fo'e ce'ai lo du'u fo'a li pa dubmau 
> kei goi dy zo'u ge ganai me'au dy gi ko'a me'au fo'e lo broda be ko'e bei 
> li mo'e fo'a vu'u pa bei fo'e gi ga me'au dy gi ko'a ko'e me'au fo'e
>
> Note that the definition is primitive recursive in its third argument. The 
> predicate yields a non-terminating computation for values in its x3 that 
> are less than or equal to zero. From this predicate, we have the following 
> relation.
>
> .i go ko'a brode lo brode be lo brode be ko'a gi ko'a ko'e broda li ci lo 
> ka [ce'u] [ce'u] brode
>
> A tentative translation of the definition to English would be difficult; I 
> will simply list how the sumti places interact without giving a definition 
> as one would expect in a dictionary.
>
> * x1, x2: arbitrary sumti of the same type
> * x3: the number of applications separating these sumti in the chain
> * x4: a binary predicate used to build the chain connecting the x1 and x2.
>
>
I'm just wonder if there needs to be both x3 and x4. Compare to dzena 
[dze], x1 is an elder/ancestor of x2 by bond/tie/degree x3. So x3 can be a 
degree such as a number or a predicate that describes the connection, e.g. 
marriage or birth.  To provide both degree and predicate, a weak possessive 
("4th marriage") would usually suffice, or a relative clause could be used. 
Is that correct for dzena? If so, wouldn't that work here too?

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<div dir=3D"ltr"><br><br>On Saturday, August 16, 2014 11:33:00 AM UTC-4, ts=
ani wrote:<blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-left:=
 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr">Our=
 motivation is the following: we want a predicate that takes two arbitrary =
sumti of the same type, a binary predicate, and a number, to construct a ch=
ain of applications of that predicate along intermediate values to "connect=
" the two sumti. This is the nature of constructs such as "great-great-gran=
dfather" and "three days from now" and "the friend of a friend of a friend =
of mine", which as we have seen through usage, are difficult to concisely e=
xpress. However, the underlying principle of all the words is the same.<br>

<br>We propose a predicate to construct such chains, of arbitrary length, d=
efined as follows in Lojban:<br><br>.i lo ka broda cu ka ko'a ko'e fo'a fo'=
e ce'ai lo du'u fo'a li pa dubmau kei goi dy zo'u ge ganai me'au dy gi ko'a=
 me'au fo'e lo broda be ko'e bei li mo'e fo'a vu'u pa bei fo'e gi ga me'au =
dy gi ko'a ko'e me'au fo'e<br>

<br>Note that the definition is primitive recursive in its third argument. =
The predicate yields a non-terminating computation for values in its x3 tha=
t are less than or equal to zero. From this predicate, we have the followin=
g relation.<br>

<br>.i go ko'a brode lo brode be lo brode be ko'a gi ko'a ko'e broda li ci =
lo ka [ce'u] [ce'u] brode<br><br>A tentative translation of the definition =
to English would be difficult; I will simply list how the sumti places inte=
ract without giving a definition as one would expect in a dictionary.<br>

<br>* x1, x2: arbitrary sumti of the same type<br>* x3: the number of appli=
cations separating these sumti in the chain<br>* x4: a binary predicate use=
d to build the chain connecting the x1 and x2.<br><br></div></blockquote><d=
iv><br></div><div>I'm just wonder if there needs to be both x3 and x4. Comp=
are to dzena [dze], x1 is an elder/ancestor of x2 by bond/tie/degree x3. So=
 x3 can be a degree such as a number or a predicate that describes the conn=
ection, e.g. marriage or birth. &nbsp;To provide both degree and predicate,=
 a weak possessive ("4th marriage") would usually suffice, or a relative cl=
ause could be used. Is that correct for dzena? If so, wouldn't that work he=
re too?</div><div><br></div></div>

<p></p>

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