The parentheses are required because =93ny. lo prenu=94 would be two se= parate sumti, =93ny.=94 and =93lo prenu=94. In general, any mathematical ex= pression other than a simple number must be in parentheses when used as a q= uantifier; the right parenthesis mark, the cmavo =93ve'o=94, can usually be= elided.

All the examples above have exhibited single lerfu words rather than le= rfu strings, in accordance with the conventions of ordinary mathematics. A = longer lerfu string would still be treated as a single variable or function= name: in Lojban, =93.abu by. cy.=94 is not the multiplication =93a =D7 b = =D7 c=94 but is the variable =93abc=94. (Of course, a local convention coul= d exist that made the value of a variable like =93abc=94, with a multi-lerf= u-word name, equal to the values of the variables =93a=94, =93b=94, and =93= c=94 multiplied together.)

All the examples above have exhibited single lerfu words rather than le= rfu strings, in accordance with the conventions of ordinary mathematics. A = longer lerfu string would still be treated as a single variable or function= name: in Lojban, =93.abu by. cy.=94 is not the multiplication =93a =D7 b = =D7 c=94 but is the variable =93abc=94. (Of course, a local convention coul= d be employed that made the value of a variable like =93abc=94, with a mult= i-lerfu-word name, equal to the values of the variables =93a=94, =93b=94, a= nd =93c=94 multiplied together.)

There is a special rule about shift words in mathematical text: shifts = within mathematical expressions do not affect lerfu words appearing outside= mathematical expressions, and vice versa.

Previous=

References to lerfu

Acronyms

diff --git a/17/13/index.html b/17/13/index.html index 2c7eaa6..56be8f7 100644 --- a/17/13/index.html +++ b/17/13/index.html @@ -18,36 +18,36 @@

List of all auxiliary lerfu-word cmavo

As Easy As A-B-C? The Lojban Letteral Syste= m And Its Uses

The Lojban Reference Gram= mar

13. Computerized character codes

Since the first application of computers to non-numerical information, = character sets have existed, mapping numbers (called =93character codes=94)= into selected lerfu, digits, and punctuation marks (collectively called = =93characters=94). Historically, these character sets have only covered the= English alphabet and a few selected punctuation marks. International effor= ts are now underway to create a unified character set that can represent es= sentially all the characters in essentially all the world=92s writing syste= ms. Lojban can take advantage of these encoding schemes by using the cmavo = =93se'e=94 (of selma'o BY). This cmavo is conventionally followed by digit = cmavo of selma'o PA representing the character code, and the whole string i= ndicates a single character in some computerized character set:

Since the first application of computers to non-numerical information, = character sets have existed, mapping numbers (called =93character codes=94)= into selected lerfu, digits, and punctuation marks (collectively called = =93characters=94). Historically, these character sets have only covered the= English alphabet and a few selected punctuation marks. International effor= ts have now created Unicode, a unified character set that can represent ess= entially all the characters in essentially all the world=92s writing system= s. Lojban can take advantage of these encoding schemes by using the cmavo = =93se'e=94 (of selma'o BY). This cmavo is conventionally followed by digit = cmavo of selma'o PA representing the character code, and the whole string i= ndicates a single character in some computerized character set:

 13.1)  me'o se'ecixa cu lerfu la .asycy'i'is.
             loi merko rupnu
        The-expression [code] 36 is-a-letteral in-set ASCII
             for-the-mass-of American currency-units.
        The character code 36 in ASCII represents American dollars.
        =93$=94 represents American dollars.

Understanding Example 13.1 depends on knowing th= e value in the ASCII character set (one of the simplest and oldest) of the = =93$=94 character. Therefore, the =93se'e=94 convention is only intelligibl= e to those who know the underlying character set. For precisely specifying = a particular character, however, it has the advantages of unambiguity and (= relative) cultural neutrality, and therefore Lojban provides a means for th= ose with access to descriptions of such character sets to take advantage of= them.

As another example, the Unicode character set (also known as ISO 10646)= represents the international symbol of peace, an inverted trident in a cir= cle, using the base-16 value 262E. In a suitable context, a Lojbanist may s= ay:

 13.2)  me'o se'erexarerei sinxa le ka panpi
        the-expression [code] 262E is-a-sign-of the quality-of being-at-pea=
ce

-When a =93se'e=94 string appears in running discourse, some metalinguistic= convention must specify whether the number is base 10 (as above) or some o= ther base, and which character set is in use. +When a =93se'e=94 string appears in running discourse, some metalinguistic= convention must specify whether the number is base 10 or some other base, = and which character set is in use.

Previous=

Acronyms

List of all auxiliary lerfu-word cmavo

commit 433c665fe0ecb06ae0f3dfd3bf37a2dfa44a6ebf Author: Robin Lee Powell Date: Tue Nov 2 18:29:29 2010 -0700 Updating chapter 16 to the red book; also one minor clarifying insertion. diff --git a/16/11/index.html b/16/11/index.html index ce8dab2..72c0d7e 100644 --- a/16/11/index.html +++ b/16/11/index.html @@ -59,21 +59,21 @@ when converted to the external negation form produces: =20 11.7) naku roda poi verba cu klama su'ode po= i ckule It is false that all children go to some school(s). In Example 11.5, we moved the negation boundary = rightward across the quantifier of =93de=94, forcing us to invert it. In Example 11.7 we moved the negation boundary across = the quantifier of =93da=94, forcing us to invert it instead. Example 11.6 merely switched the selbri and the negation bounda= ry, with no effect on the quantifiers.

The same rules apply if you rearrange the sentence so that the quantifi= er crosses an otherwise fixed negation. You can=92t just convert the selbri= of Example 11.4 and rearrange the sumti to produ= ce

 11.8)  su'ode poi ckule ku'o naku se klama ro=
da poi verba
        Some schools aren=92t gone-to-by every child.

-or rather, Example 11.8 means something complete= ly different from Example 11.4. Conversion with = =93se=94 under =93naku=94 negation is not symmetric; not all sumti are trea= ted identically, and some sumti are not invariant under conversion. These c= omplications would make Lojban much harder to learn (just as their correspo= nding natural language constructs are difficult to learn). Thus, internal n= egation with =93naku=94 is considered an advanced technique, used to achiev= e stylistic compatibility with natural languages. +or rather, Example 11.8 means something complete= ly different from Example 11.4. Conversion with = =93se=94 under =93naku=94 negation is not symmetric; not all sumti are trea= ted identically, and some sumti are not invariant under conversion. Thus, = internal negation with =93naku=94 is considered an advanced technique, used= to achieve stylistic compatibility with natural languages.

It isn=92t always easy to see which quantifiers have to be inverted in = a sentence. Example 11.4 is identical in meaning = to:

 11.9)  su'o verba naku klama su'o ckule
        Some children don=92t go-to some school.

but in Example 11.9, the bound variables =93da= =94 and =93de=94 have been hidden.

It is trivial to export an internal bridi negation expressed with =93na= =94 to the prenex, as we saw in Section 9; you just m= ove it to the left end of the prenex. In comparison, it is non-trivial to e= xport a =93naku=94 to the prenex because of the quantifiers. The rules for = exporting =93naku=94 require that you export all of the quantified variable= s (implicit or explicit) along with =93naku=94, and you must export them fr= om left to right, in the same order that they appear in the sentence. Thus = Example 11.4 goes into prenex form as:

 11.10) su'oda poi verba ku'o naku
             su'ode poi ckule zo'u da klama de
diff --git a/16/12/index.html b/16/12/index.html
index d8e8fe5..e1bcbe8 100644
--- a/16/12/index.html
+++ b/16/12/index.html
@@ -63,22 +63,22 @@ The =93ga=94 and =93gi=94, meaning =93either-or=94, hav=
e become =93ge=94 and =93
 And by dividing the bridi with logically connected selbri into two bridi,
  12.7)  naku zo'u ge la djein. le zarci cu dzu=
kla
             gi la djein. le zarci cu bajrykla
        It-is-false-that: both (Jane to-the market walks)
             and (Jane to-the market runs).
 
 is the result.
 At this expanded level, we apply DeMorgan=92s Law to distribute the neg=
ation in the prenex across both sentences, to get
 -12.8)  ga la djein. le zarci cu na dzukla
-            gi la djein. le zarci cu na bajrykla
+12.8)  ga la djein. le zarci na dzukla
+            gi la djein. le zarci na bajrykla
        Either Jane to-the market [false] walks,
             or Jane to-the market [false] runs.
 
 which is the same as
  12.9)  ganai la djein. le zarci cu dzukla
             ginai la djein. le zarci cu bajrykla
        If Jane to-the market walks,
             then Jane to-the market [false] runs.
        If Jane walks to the market, then she doesn=92t run.
diff --git a/16/13/index.html b/16/13/index.html
index 7ab5ac5..de59827 100644
--- a/16/13/index.html
+++ b/16/13/index.html
@@ -24,21 +24,21 @@

13. selbri variables

In addition to the variables =93da=94, =93de=94, and =93di=94 that we h= ave seen so far, which function as sumti and belong to selma'o KOhA, there = are three corresponding variables =93bu'a=94, =93bu'e=94, and =93bu'i=94 wh= ich function as selbri and belong to selma'o GOhA. These new variables allo= w existential or universal claims which are about the relationships between= objects rather than the objects themselves. We will start with the usual s= illy examples; the literal translation will represent =93bu'a=94, =93bu'e= =94 and =93bu'i=94 with F, G, and H respectively.

 13.1)  su'o bu'a zo'u la djim. bu'a la djan.
        For-at-least-one relationship-F : Jim stands-in-relationship-F to-J=
ohn.
        There=92s some relationship between Jim and John.

The translations of Example 13.1 show how uni= diomatic selbri variables are in English; Lojban sentences like Example 13.1 need to be totally reworded in English. Further= more, when a selbri variable appears in the prenex, it is necessary to prec= ede it with a quantifier such as =93su'o=94; it is ungrammatical to just sa= y =93bu'a zo'u=94. This rule is necessary because only sumti can appear in = the prenex, and =93su'o bu'a=94 is technically a sumti =97 in fact, an inde= finite description like =93re nanmu=94, since =93bu'a=94 is grammatically e= quivalent to a brivla like =93nanmu=94. However, indefinite descriptions in= volving the bu'a-series cannot be imported from the prenex.

The translations of Example 13.1 show how uni= diomatic selbri variables are in English; Lojban sentences like Example 13.1 need to be totally reworded in English. Further= more, when a selbri variable appears in the prenex, it is necessary to prec= ede it with a quantifier such as =93su'o=94; it is ungrammatical to just sa= y =93bu'a zo'u=94. This rule is necessary because only sumti can appear in = the prenex, and =93su'o bu'a=94 is technically a sumti =97 in fact, it is a= n indefinite description like =93re nanmu=94, since =93bu'a=94 is grammatic= ally equivalent to a brivla like =93nanmu=94. However, indefinite descripti= ons involving the bu'a-series cannot be imported from the prenex.

When the prenex is omitted, the preceding number has to be omitted too:=

 13.2)  la djim. bu'a la djan.
        Jim stands-in-at-least-one-relationship to-John.

As a result, if the number before the variable is anything but =93su'o=94,= the prenex is required:

 13.3)  ro bu'a zo'u la djim. bu'a la djan.
        For-every relationship-F : Jim stands-in-relationship-F to-John.
        Every relationship exists between Jim and John.
diff --git a/16/9/index.html b/16/9/index.html
index 6059098..212d9ff 100644
--- a/16/9/index.html
+++ b/16/9/index.html
@@ -116,21 +116,21 @@ which is negated by:
  9.14)  naku noda rode zo'u da prami de
        It is false that: there is no X that, for every Y, X loves Y.
        It is false that there is nobody who loves everything.
 
 We can simplify Example 9.14 by transforming =
the prenex. To move the negation phrase within the prenex, we must first ex=
pand the =93no=94 quantifier. Thus =93for no x=94 means the same thing as =
=93it is false for some x=94, and the corresponding Lojban =93noda=94 can b=
e replaced by =93naku su'oda=94. Making this substitution, we get:
  9.15)  naku naku su'oda rode zo'u da prami =
de
        It is false that it is false that: for an X, for every Y: X loves Y=
.
 
-Adjacent double negation boundaries in the prenex can be dropped, so this =
means the same as:
+Adjacent pairs of negation boundaries in the prenex can be dropped, so thi=
s means the same as:
  9.16)  su'oda rode zo'u da prami de
        There is an X such that, for every Y, X loves Y.
        At least one person loves everything.
 
 which is clearly the desired contradiction of Exampl=
e 9.13.
 The interactions between quantifiers and negation mean that you cannot =
eliminate double negatives that are not adjacent. You must first move the n=
egation phrases so that they are adjacent, inverting any quantifiers they c=
ross, and then the double negative can be eliminated.
 
 
 

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