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?