Toward a quantitative form of Lojban
ckinytadji selsku
- fy. fancu lo'i ni terzu'e lo'i ni selsnada .ije li ma'o fy.boi du'e du li mo'a How can we express "Too many goals means too few accomplishments" in a quantitative form?
- fancu le'i nu funca It depends on luck.
ckinytadji vlaselcmi
math terminology proposes some technical terms, but it's light on words that are useful in everyday life. I think there are plenty; I'm starting this list. mi'e jezrax (I think xod added most of this.)
- selcmi, klesi (sets)
- superset - selkle
- set, subset - klesi
- proper subset - nalrolmeilei (from the jvoste)
- cmima x1 is a member of set x2 [x1 may be a complete or incomplete list of members; x2 is normally marked by la'i/le'i/lo'i, defining the set in terms of its common property(ies), though it may be a complete enumeration of the membership];
- gripau x1 is a subset of set x2 [girzu pagbu, set-part]
- disjoint -
- overlapping (with non-empty intersection) -
Note: klesi is a set defined by a rule; selcmi is a set defined by its membership.
- fancu (functions)
- monotonically increasing - farstodi zenba
- monotonically decreasing - farstodi jdika
- bounded above - galseljimte
- bounded below - dziseljimte
- cuncmaci (statistics)
- statistically independent -
- correlated -
- fadytercu'o x1 = cunso3 (set) follows a Gaussian probability distribution with independent variable x2 = cunso
- Simple relationships (zbepi terki'i)
- du x1 is identical to x2, x3, x4, ...
- dunli x1 is equal/congruent to x2 in/on property/quality/dimension/quantity x3 [same in quantity/quality (not necessarily in identity); 'analogy' may be expressed as the equivalence of two properties of similarity (ka x1 simsa x2) and (ka x3 simsa x4)] (.ua zo du cu dunli jenai du zo dunli .i le si'o du kei cu du le si'o dunli fi ko le ka bu'a)
- mleca x1 is less than x2 in property/quantity x3 (ka/ni) by amount x4 [also negative (= nonme'a)];
- jdika x1 (experiencer) decreases/contracts/is reduced/diminished in property/quantity x2 by amount x3
- zmadu x1 is greater than x2 [also positive (= nonmau)];
- zenba x1 (experiencer) increases/is incremented/augmented in property/quantity x2 by amount x3
- dubjavme'a x1 is less than or equal to x2 [du ja mleca, equal or less]
- or nalmau x1 is not greater than x2
- dubjavmau x1 is greater than or equal to x2 [du ja zmadu, equal or greater]
- or nalme'a x1 is not less than x2
- tamdu'i x1 is similar to x2 [tarmi dunli, shape-equal]
- turdu'i x1 is isomorphic to x2 [stura dunli, structure-equal]
- pabdu'i x1 is proportional to x2 [parbi dunli, ratio-equal]
- na'ujbi x1 is approximately equal to [namcu jibni, number-near]
- lamji x1 is adjacent/beside/next to/in contact with x2 in property/sequence x3 in direction x4 [also touching, contiguous, against];
- Assorted useful brivla (vrici selpli brivla)
- fancu x1 is a function/single-valued mapping from domain x2 to range x3 defined by expression/rule x4 (ru'a le fancu cu cmene le velfancu)
- manri x1 is a frame of reference/standard for observing/measuring/determining x2, with/by rules x3
- ckilu x1 (si'o) is a scale of units for measuring/observing/determining x2 (state)
- cimde x1 (property - ka) is a dimension of space/object x2 according to rules/model x3
- morna x1 is/reflects/represents a pattern of forms/events x2 arranged according to structure x3 [x3 is a [[model] for x1 (= termontai, or the more abstract = termonsi'o);
- mokca x1 is a point/instant/moment [0-dimensional shape/form] in/on/at time/place x2
- linji x1 is a line/among lines [1-dimensional shape/form] defined by set of points x2. [ray/vector (farli'i or porli'i)]
- plita x1 is a plane [2-dimensional shape/form] defined by points x2 (set); x1 is flat/[smooth]. [also: x1 is even/planar/level]; (x2 is a set of points at least sufficient to define the plane)
- canlu x1 is space/volume/region/room [at-least-3-dimensional area] occupied by x2. [also occupy (= selca'u)]
- Logical Inference (see logical induction & deduction)
- deduction: nibli, ja'o
- induction: sucta, su'a
- abduction: tolsucta, su'anai
ckinytadji nalca'ima'o
- 'ja'axi [NA]:' bridi truth value scalar
- 'xoi'a [PU]:' increasing linearly over time
- la papri xoi'a pelxu The page is yellowing.
- 'xoi'e [PU]:' exponential increasing
- do xoi'e lojbo certu You're learning Lojban at an exponential rate.
- Semantically, xoi'a/xoi'e belong in ZAhO, since they deal with change in truth over time. For example, co'a is change from categorically false to categorically true. xoi'a/xoi'e deal with rates of increase in degree of truth. However, there are several possible rates of increase, and there is also the possibility of decrease, so I think this domain of meaning requires some more comprehensive proposal than simply these two cmavo. --And