BPFK Section: Inexact Numbers: Difference between revisions

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m (Text replace - "jbocre: ([L-Z])" to "$1")
m (Text replace - "jbocre: ([a-z])" to "$1")
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generic | ::no [[no'o|no'o]] ro::
generic | ::no [[no'o|no'o]] ro::


subjective |  :: [[mo'a|mo'a]]  [[jbocre: rau|rau]]  [[du'e|du'e]]::
subjective |  :: [[mo'a|mo'a]]  [[rau|rau]]  [[du'e|du'e]]::


'''ranges'''
'''ranges'''

Revision as of 15:02, 23 March 2014

Proposed definitions

su'o (PA)
At least (one). Some.

so'e lo ponjo jugle'u cu lerfu fi su'o re lo se bacru


Most Japanese kanji have at least two pronunciations.

su'e (PA)
At most (one).

la cibyska cu se kelci su'e bi remna


Tricolor is played by at most eight people.

za'u (PA)
More than (one).

ko za'u re'u troci


Try again!

me'i (PA)
Less than (all). Not all.

me'i gerku cu klama lo cevzda


Not all dogs go to heaven.

ji'i (PA)
Approximately.

ji'i xa pi xa gigdo be lo remna cu xabju la terdi


Approximately 6.6 billion humans inhabit the Earth.

ro (PA)
Each. All. Every.

lo srasu ro roi ri'ozma ze'o lo bitmu


The grass is always greener on the other side of the fence.

da'a (PA)
All except (one).

da'a drata cu ci pa mei


All but one of the others are thirty-one-somes.

so'a (PA)
Almost all. All but a few.

do so'a roi lerci


You're almost always late.

so'e (PA)
Most. All but a significant number.

ta so'e mei


That's most of them.

so'i (PA)
Many. A large number.

mi ba'o cilre so'i da lo xirma lo vi cukta


I have learned a lot about horses from this book.

so'o (PA)
Several. A significant number.

so'o lo pendo be mi cu simlu lo ka jinvi lo du'u xamgu sidbo


Several of my friends seem to think it's a good idea.

so'u (PA)
A few. A small number.

mi stali lo darno ze'a lo masti be li so'u


I stayed away for a few months.

no'o (PA)
A vague number. Some number. A certain number.

ba lo mentu be li no'o lo minji cu sisti


After some number of minutes, the machine stopped.

rau (PA)
Enough. The right number.

xu do pu snada lo nu cpacu lo rau kelci


Did you manage to get enough players?

du'e (PA)
Too many. More than the right number.

du'e cuntu ka'e fliba


Too many things could go wrong.

mo'a (PA)
Too few. Less than the right number.

mi'a mo'a roi casnu lo ckape


We discussed the dangers too few times.

Formal definitions

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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

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Quantifiers

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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

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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

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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

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piPA sumti | lo piPA si'e be sumti

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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:

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piPA sumti | lo piPA si'e be pa me sumti

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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".

Issues