View source for UserWiki:Ilmen/two paradigm candidates for amount abstraction predicates

== TWO PARADIGM CANDIDATES FOR AMOUNT PREDICATES ==

Let us call "amount predicate" any predicate that involves an amount abstraction, such as {mutce}, {traji}, {zenba}, {zmadu}, {cnano}, {zilzena} and so on.

By the past, Lojbanists used to use them in the following manner:

Ⓐ {mi mutce lo ni ce'u tatpi}, {mi traji lo ni ce'u certu}.

But this usage of {ni} was conflicting and incompatible with another usage thereof, namely a relation between a pure number and a proposition:

Ⓑ {li no ni mi tatpi}, {lo mitre be li re ni ta rajycla}

Those sentences are equivalent to ones using a numeric amount predicate such as the hypothetical "rajyclalai": "x1 has a tallness of x2 (number)". For example:

Ⓒ {ta rajyclalai li re}

The current trend is to use {ni} only with that second meaning, and thus, by the Lojban design rule that cmavo shall not display any polysemy that the syntactic environment cannot resolve, the usage of {ni} with amount predicates as illustrated in Ⓐ should be forbidden.

That raises the question of what kind of argument should be provided to amount predicates.

There are two competing possible paradigms, we shall introduce them below.


=== — PARADIGM 1 — ===

Amount slots can be any of the following depending on the predicate's definition:

• An abstract relation between an entity and a number, for example {lo ka ce'u se majga ce'u}, "the relation [___ is the mass of ___]" (that would be suitable for mutce-x2, zenba-x2, traji-x2 etc.) ;

• An abstract property of a number, e.g. {lo ka ce'u majga ti} ("the property [___ is the mass of this]" (that would be suitable for zilzena-x1).

Example of usage:

Ⓓ {mi zenba lo ka ce'u tiljylai ce'u}, "I increase in weight",
  {lo ka do rajyclalai ce'u cu zilzena}, "your tallness increases",
  {mi traji lo ka ce'u citka mo'e ce'u da}, "I'm the one who ate the greatest number of things".

The downside of this paradigm is that there are often two {ce'u}s, which can make things longer, and Lojban doesn't have many numeric amount predicates like {rajyclalai} with a number slot directly in their argument structure. Using {la'u} together with a regular relative greatness predicate (rajycla instead of rajyclalai, tsali instead of tsalai…) is an alternative: {mi mutce lo ka ce'u tsali se la'u ce'u}. {lo ka ni…} has also been sometimes used.

The upside of this paradigm is that having a numeric ce'u-slot allows saying things like {zenba lo ka ce'u viska mo'e ce'u da}. Giving a formal definition for amount predicates becomes fairly easy, for example {zmadu} can be defined as follow:
{lo se ckini be x1 bei x3 cu dubmau lo se ckini be x2 bei x3}, "what x1 is in relation x3 with is a number greater than what x2 is in relation x3 with".

Furthermore, the number slot can appear arbitrarily deeply nested in the abstraction.

=== — PARADIGM 2 — ===

Amount slots are either properties or propositions. No pure number slot is directly involved, the predicate in the abstraction is a "greatness predicate" such as {tsali}, {rajycla}, {glare} and so on, as opposed to their numeric amount predicate equivalents, {tsalai}, {rajyclalai}, {glalai} respectively, as is the case with Paradigm 1.

Example of usage:

Ⓔ {mi zenba lo ka ce'u tilju}, "I increase in weight",
  {lo du'u do rajycla cu zilzena}, "your tallness increases",
  {mi traji lo ka ru'o se citka be ce'u cu sormei}, "I'm the one who ate the greatest number of things".

(Note that the third example in Ⓔ is worded significantly differently from its equivalent in Ⓓ.)

The upside of this paradigm is that less {ce'u} slots are necessary, which makes for more succintness, and it directly makes use of the Lojban stock of greatness predicates, without requiring {la'u} or the creation of equivalent numeric amount predicates as is the case with Paradigm 1.

The downside is that giving a formal definition for amount predicates under this paradigm is more challenging. There seems to be a need for some sort of magical predicate that would allow converting any proposition or property with a greatness predicate (e.g. tsali, rajycla…) as its main predicate into something that allow extracting a concrete number out of it for making comparisons (e.g. for defining {zmadu}).

A possible formal definition for {zmadu} under this paradigm could be:
{lo *** be x3 cu poi'i lo se ckini be x1 bei ke'a cu dubmau lo se ckini be x2 bei ke'a}, "with R being the numeric predicate relation corresponding to the greatness property x3, what x1 is in relation R with is a number greater than what x2 is in relation R with".
(«***» here stands for the aforementioned magical conversion predicate.)

Whether the necessity of such a conversion predicate really poses a significant problem for e.g. developping interpretation software remains to be investigated. That might be no more troublesome than interpreting other magical-looking predicates such as {bridi}, after all.

----

''(Ilmen, 2018-01-19)''