History: BPFK Section: Inexact Numbers

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Proposed definitions

su'o (PA)
At least (one).
su'e (PA)
At most (one).
za'u (PA)
More than (one).
me'i (PA)
Less than (all).
ji'i (PA)
Approximately.

ro (PA)
Each. All. Every.
da'a (PA)
All except (one).
so'a (PA)
Almost all. All but a few.
so'e (PA)
Most. All but a significant number.
so'i (PA)
Many. A large number.
so'o (PA)
Several. A significant number.
so'u (PA)
A few. A small number.
no'o (PA)
A vague number. Some number. A certain number.

rau (PA)
Enough. The right number.
du'e (PA)
Too many. More than the right number.
mo'a (PA)
Too few. Less than the right number.

Formal definitions

su'o PA vei na'u zmadu ja dunli PA
su'e PA vei na'u mleca ja dunli PA
za'u PA vei na'u zmadu PA
me'i PA vei na'u mleca PA
ji'i PA vei na'u jibni PA
da'a PA vei na'u se sumji be lo mulno PA
ro vei ni'e mulno
so'a vei ni'e muljbi
so'e vei ni'e xabmau
so'i vei ni'e mutce
so'o vei ni'e milxe
so'u vei ni'e toltce
rau vei ni'e drani
du'e vei ni'e dukse
mo'a vei ni'e toldu'e
no'o vei ni'e co'e


Quantifiers

definite
no pa re ci vo mu xa ze bi ... da'aci da'are da'apa ro
scalar
no [ so'u ] [ so'o ] [ so'i ] [ so'e ] [ so'a ] ro
generic
no [ no'o ] ro
subjective
[ mo'a ] [ rau ] [ du'e ]
ranges
su'o PA
.......................... [PA ............................]
za'u PA
.......................... PA [............................]
su'e PA
[......................... PA] .............................
me'i PA
[.........................] PA .............................
ji'i PA
................... [...... PA ......] ........................

da'a
da'a da'a PA PA
da'a ro no
da'a so'a so'u
da'a so'e so'o
da'a so'i so'i
da'a so'o so'e
da'a so'u so'a
da'a no ro
da'a rau rau
da'a du'e mo'a
da'a mo'a du'e
da'a no'o no'o
da'a su'o PA su'e da'a PA
da'a su'e PA su'o da'a PA
da'a za'u PA me'i da'a PA
da'a me'i PA za'u da'a PA
da'a ji'i PA ji'i da'a PA


Definitions in terms of su'o:
su'o N+1 da zo'u da broda su'o da su'o N de zo'u ge da na du de gi da .e de broda
za'u N da su'o N+1 da
su'e N da naku su'o N+1 da
me'i N da naku su'o N da
N da su'o N da .enai su'o N+1 da
da'a PA da PA da naku


In particular:

no da = me'ipa da = naku su'o da
ro da = da'ano da = no da naku = naku su'o da naku

With restricted da (i.e. da poi broda):
su'o da poi broda cu brode su'o da zo'u da broda gi'e brode
su'o N da poi broda cu brode su'o N da zo'u da broda gi'e brode
za'u N da poi broda cu brode za'u N da zo'u da broda gi'e brode
su'e N da poi broda cu brode su'e N da zo'u da broda gi'e brode
me'i N da poi broda cu brode me'i N da zo'u da broda gi'e brode
N da poi broda cu brode N da zo'u da broda gi'e brode
da'a Q da poi broda cu brode da'a Q da zo'u da broda nagi'a brode

Internal grammar of quantifiers

quantifier proportional / fractional
fractional [prefix] pi (indefinite / definite / prefix)
proportional simple & simple [fi'u (ro & definite) / ce'i]
simple prefix & (indefinite / definite)
prefix da'a & (su'o / su'e / me'i / za'u / ji'i) & da'a
indefinite so'u / so'o / so'i / so'e / so'a / ro / mo'a / rau / du'e / no'o
definite (no / pa / re / ci / vo / mu / xa / ze / bi / so / ki'o) ...


[ ] indicates the enclosed element is optional
... indicates the preceding element may appear one or more times
/ indicates either the preceding or the following element may appear
& indicates the preceding, the following or both elements may appear

Defaults for bare prefix

When a prefix is not followed by a definite or indefinite, a default value is understood: the default is pa for su'o, su'e, za'u and da'a; ro for me'i; and a vague number (perhaps no'o) for ji'i.

Two adjacent simple quantifiers

  • Two adjacent simple quantifiers are interpreted, when possible, as if joined with .e:


ro ci broda
all three brodas, all brodas and three brodas.

rau su'o mu broda
enough at least five brodas, enough brodas and at least five brodas.

su'o ci su'e bi broda
at least three at most eight brodas
at least three brodas and at most eight brodas
between three and eight brodas (inclusive)

  • Two adjacent simple quantifiers are interpreted, when joining them with .e would give a contradiction, as if joined with .a:


me'i ci za'u ci broda
less than three more than three brodas
less than three brodas or more than three brodas
i.e. other than three brodas

mo'a du'e broda
too few too many brodas
too few brodas or too many brodas
the wrong number of brodas

Proportional quantifiers


re fi'u ci broda
Two out of every three brodas.
Two thirds of brodas.

za'u vo fi'u mu broda
More than four out of every five brodas.
More than four fifths of brodas.

du'a fi'u ro muno broda
Too many out of all 50 broda.
Too many broda, of which there are 50 in all.

  • ce'i is equivalent to fi'u panono:


za'u munoce'i broda
More than half of all brodas.

da'a cirepimu ce'i broda
All but 32.5% of brodas.

Fractional quantifiers

piPA sumti lo piPA si'e be sumti


When a sumti has a single referent (which may be a simple individual, a group, a set, etc.) then a fractional quantifier refers to a corresponding fraction of the referent. In particular, a fraction of a group or a set is a subgroup or subset whose cardinality is the corresponding fraction of the cardinality of the whole.

When a sumti has more than one referent (e.g. le ci plise) then a fractional quantifier refers to a fraction of one (which one is not specified) of the referents. Then pimu le ci plise is "half of one of the three apples. Then more generally we can define:

piPA sumti lo piPA si'e be pa me sumti


which will also cover the case of a single referent.

We may then generalize to things like repimu le ci plise for "two and a half of the three apples".

History

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Mon 10 of Nov, 2014 22:40 GMT durka42 from 158.130.106.110 fixed negation rule formatting 26
Thu 21 of Aug, 2014 14:30 GMT Ilmen from 95.210.209.219 Adding a couple of word links. 25
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Tue 17 of Jun, 2014 21:48 GMT selpa'i from 93.220.99.115 18
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Fri 06 of Jun, 2014 16:40 GMT Ilmen from 213.180.252.213 PA -> PA# 14
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