Lojban is a logical language: the name of the language itself means =93= logical language=94. The fundamentals of ordinary logic (there are variant = logics, which aren=92t addressed in this book) include the notions of a =93= sentence=94, (sometimes called a =93statement=94 or =93proposition=94), whi= ch asserts a truth or falsehood, and a small set of =93truth functions=94, = which combine two sentences to create a new sentence. The truth functions h= ave the special characteristic that the truth value (that is, the truth or = falsehood) of the results depends only on the truth value of the component = sentences. For example,

Lojban is a logical language: the name of the language itself means =93= logical language=94. The fundamentals of ordinary logic (there are variant = logics, which aren=92t addressed in this book) include the notions of a =93= sentence=94 (sometimes called a =93statement=94 or =93proposition=94), whic= h asserts a truth or falsehood, and a small set of =93truth functions=94, w= hich combine two sentences to create a new sentence. The truth functions ha= ve the special characteristic that the truth value (that is, the truth or f= alsehood) of the results depends only on the truth value of the component s= entences. For example,

We will use the phrase =93negating a sentence=94 to mean changing its t= ruth value. An English sentence may always be negated by prefixing =93It is= false that ... =94, or more idiomatically by inserting =93not=94 at the ri= ght point, generally before the verb. =93James is not a woman=94 is the neg= ation of =93James is a woman=94, and vice versa. Recent slang can also nega= te a sentence by following it with the exclamation =93Not!=94

Words like =93or=94 are called =93logical connectives=94, and Lojban ha= s many of them, as befits a logical language. This chapter is mostly concer= ned with explaining the forms and uses of the Lojban logical connectives. T= here are a number of other logical connectives in English such as =93and=94= , =93and/or=94, =93if=94, =93only if=94, =93whether or not=94, and others; = however, not every use of these English words corresponds to a logical conn= ective. This point will be made clear in particular cases as needed. The ot= her English meanings are supported by different Lojban connective construct= s.

The Lojban connectives form a system (as the title of this chapter sugg= ests), regular and predictable, whereas natural-language connectives are ra= ther less systematic and therefore less predictable.

There exist 16 possible different truth functions. A truth table is a g= raphical device for specifying a truth function, making it clear what the v= alue of the truth function is for every possible value of the component sen= tences. Here is a truth table for =93or=94:

It suffices to note here, then, a few purely grammatical points about t= anru logical connection. =93bo=94 may be appended to jeks as to eks, with t= he same rules:

Forethought tanru connection does not use geks, but uses guheks instead= . Guheks have exactly the same form as geks:

13. Truth questions and connective questions

So far we have addressed only sentences which are statements. Lojban, l= ike all human languages, needs also to deal with sentences which are questi= ons. There are many ways of asking questions in Lojban, but some of these (= like questions about quantity, tense, and emotion) are discussed in other c= hapters.

The simplest kind of question is of the type =93Is it true that ... =94= where some statement follows. This type is called a =93truth question=94, = and can be represented in English by Example 13.1= :

A truth question can be answered =93yes=94 or =93no=94, depending on th= e truth or falsity, respectively, of the underlying statement. The standard= way of saying =93yes=94 in Lojban is =93go'i=94 and of saying =93no=94 is = =93nago'i=94. (The reasons for this rule are explained in Chapter 7.) In answer to Example 13.2, = the possible answers are:

Like all non-logical connectives, the usage shown in Example 15.7 cannot be mechanically converted into a non-logical co= nnective placed at another location in the bridi. The forethought equivalen= t of Example 15.7 is:

Non-logical forethought termsets are also useful when the things to be = non-logically connected are sumti preceded with tense or modal (BAI) tags:<= /p>

Joiks may be prefixed with =93.i=94 to produce ijoiks, which serve to n= on-logically connect sentences. The main known use here is =93.ice'o=94, wh= ich indicates that the event of the second bridi follows that of the first = bridi in some way other than a time relationship (which is handled with a t= ense):

Joiks may be prefixed with =93.i=94 to produce ijoiks, which serve to n= on-logically connect sentences. The ijoik =93.ice'o=94 indicates that the e= vent of the second bridi follows that of the first bridi in some way other = than a time relationship (which is handled with a tense):

You can also combine two operands with =93ce'o=94, the sequence connect= ive of selma'o JOI, to make a compound subscript:

Previous=

Interval connectives and forethought non-l= ogical connection

Tenses, modals, and logical connection

diff --git a/14/18/index.html b/14/18/index.html index dd93657..e5f60cb 100644 --- a/14/18/index.html +++ b/14/18/index.html @@ -18,21 +18,21 @@

Abstractor connection and connection withi= n abstractions

If Wishes Were Horses: The Lojban Connectiv= e System

The Lojban Reference Gram= mar

18. Tenses, modals, and logical connection

The tense and modal systems of Lojban interact with the logical connect= ive system. No one chapter can explain all of these simultaneously, so each= chapter must present its own view of the area of interaction with emphasis= on its own concepts and terminology. In the examples of this chapter, the = many tenses of various selma'o as well as the modals of selma'o BAI are sim= plified to the simple time cmavo =93pu=94, =93ca=94, and =93ba=94 (of selma= 'o PU) representing the past, the present, and the future respectively. Pre= ceding a selbri, these cmavo state the time when the bridi was, is, or will= be true (analogous to English verb tenses); preceding a sumti, they state = that the event of the main bridi is before, simultaneous with, or after the= event given by the sumti (which is generally a =93le nu=94 abstraction; se= e Chapter 11).

The tense and modal systems of Lojban interact with the logical connect= ive system. No one chapter can explain all of these simultaneously, so each= chapter must present its own view of the area of interaction with emphasis= on its own concepts and terminology. In the examples of this chapter, the = many tenses of various selma'o as well as the modals of selma'o BAI are rep= resented by the simple time cmavo =93pu=94, =93ca=94, and =93ba=94 (of selm= a'o PU) representing the past, the present, and the future respectively. Pr= eceding a selbri, these cmavo state the time when the bridi was, is, or wil= l be true (analogous to English verb tenses); preceding a sumti, they state= that the event of the main bridi is before, simultaneous with, or after th= e event given by the sumti (which is generally a =93le nu=94 abstraction; s= ee Chapter 11).

The two types of interaction between tenses and logical connectives are= logically connected tenses and tensed logical connections. The former are = fairly simple. Jeks may be used between tense cmavo to specify two connecte= d bridi that differ only in tense:

 18.1)  la .artr. pu nolraitru
             .ije la .artr. ba nolraitru
        Arthur [past] is-a-noblest-governor.
             And Arthur [future] is-a-noblest-governor.
        Arthur was a king, and Arthur will be a king.

can be reduced to:

diff --git a/14/20/index.html b/14/20/index.html
index 33cdea4..dbc5873 100644
--- a/14/20/index.html
+++ b/14/20/index.html
@@ -23,21 +23,22 @@
 The Lojban Reference Gram=
mar

20. Constructs and appropriate connectives

The following table specifies, for each kind of construct that can be l= ogically or non-logically connected in Lojban, what kind of connective is r= equired for both afterthought and (when possible) forethought modes. An ast= erisk (*) indicates that tensed connection is permitted.

21. Truth functions and corresponding logical connectives

The following table specifies, for each truth function, the most-often = used compound cmavo which expresses it for each of the six types of logical= connective. (Other compound cmavo are often possible: for example, =93se.a= =94 means the same as =93a=94, and could be used instead.)

The following table specifies, for each truth function, the most-often = used cmavo or compound cmavo which expresses it for each of the six types o= f logical connective. (Other compound cmavo are often possible: for example= , =93se.a=94 means the same as =93a=94, and could be used instead.)

22. Rules for making logical and non-logical connectives

The full set of rules for inserting =93na=94, =93se=94, and =93nai=94 i= nto any connective is:

first	second	third	result
True	True	True
True	False	True

construct	afterthought	afterthought +logical	forethought logical	afterthought non-logical	forethought non-logical
bridi	ijek*

Previous=

Truth functions and corresponding logical = connectives

Locations of other tables

diff --git a/14/3/index.html b/14/3/index.html index ff87652..b1796f8 100644 --- a/14/3/index.html +++ b/14/3/index.html @@ -29,21 +29,21 @@

Consider the English sentence:

 3.1)   Mary went to the window and  ...

where the last word could be followed by =93the door=94, a noun phrase, or= by =93saw the horses=94, a sentence with subject omitted, or by =93John we= nt to the door=94, a full sentence, or by one of a variety of other English= grammatical constructions. Lojban cannot tolerate such grammatical loosene= ss.

Instead, there are a total of five different selma'o used for logical c= onnection: A, GA, GIhA, GUhA, and JA. Each of these includes four cmavo, on= e based on each of the four vowels, which is always the last vowel in the c= mavo. In selma'o A, the vowel is the entire cmavo.

Thus, in selma'o A, the cmavo for the function A is =93a=94. (Do not confuse A, which is a selma'o, with A, which is a truth function, or =93a=94, which is a cmavo.) L= ikewise, the cmavo for E in selma'o GIhA is =93g= i'e=94, and the cmavo for U in selma'o GA is =93= gu=94. This systematic regularity makes the cmavo easier to learn.

Obviously, four cmavo are not enough to express the 14 truth functions = explained in Section 1. Therefore, compound cmavo mus= t be used. These compound cmavo follow a systematic pattern: each has one c= mavo from the five logical connection selma'o at its heart, and may also co= ntain one or more of the auxiliary cmavo =93se=94, =93na=94, or =93nai=94. = Which auxiliaries are used with which logical connection cmavo, and with wh= at grammar and meaning, will be explained in the following sections. The us= es of each of these auxiliary cmavo relates to its other uses in other part= s of Lojban grammar.

For convenience, each of the types of compound cmavo used for logical c= onnection is designated by a Lojban name. The name is derived by changing t= he final =93-A=94 of the selma'o name to =93-ek=94; the reasons for using = =93-ek=94 are buried deep in the history of the Loglan Project. Thus, compo= und cmavo based on selma'o A are known as eks, and those based on selma'o J= A are known as jeks. (When writing in English, it is conventional to use = =93eks=94 as the plural of =93ek=94.) When the term =93logical connective= =94 is used in this chapter, it refers to one or more of these kinds of com= pound cmavo.

Why does the title of this section refer to =93six types=94 when there = are only five selma'o? A jek may be preceded by =93.i=94, the usual Lojban = cmavo for connecting two sentences. The compound produced by =93.i=94 follo= wed by a jek is known as an ijek. It is useful to think of ijeks as a sixth= kind of logical connective, parallel to eks, jeks, geks, giheks, and guhek= s.

There also exist giks, joiks, ijoiks, and joigiks, which are not logica= l connectives but are other kinds of compound cmavo which will be introduce= d later.

There also exist giks, joiks, ijoiks, and joigiks, which are not logica= l connectives, but are other kinds of compound cmavo which will be introduc= ed later.

Previous<= /div>

The Four basic vowels

Logical connection of bridi

diff --git a/14/4/index.html b/14/4/index.html index 63826ee..f503c4a 100644 --- a/14/4/index.html +++ b/14/4/index.html @@ -61,28 +61,28 @@ The meaning of both Example 4.5 and Ex John is-a-man or James is-not-a-woman. John is a man if James is a woman. How=92s that again? Are those two English sentences in Example 4.8 really equivalent? In English, no. The Lojban TTFT truth = function can be glossed =93A if B=94, but the =93if=94 does not quite have = its English sense. Example 4.8 is true so long as = John is a man, even if James is not a woman; likewise, it is true just beca= use James is not a woman, regardless of John=92s gender. This kind of =93if= -then=94 is technically known as a =93material conditional=94.

Since James is not a woman (by our assertions in Sect= ion 1), the English sentence =93John is a man if James is a woman=94 se= ems to be neither true nor false, since it assumes something which is not t= rue. It turns out to be most convenient to treat this =93if=94 as TTFT, whi= ch on investigation means that Example 4.8 is true= . Example 4.9, however, is equally true:

 4.9)   la djan. ninmu .ijanai la djeimyz. nin=
mu
        John is a woman if James is a woman.

This can be thought of as a principle of consistency, and may be paraphras= ed as follows: =93If a false statement is true, any statement follows from = it.=94 All uses of English =93if=94 must be considered very carefully when = translating into Lojban to see if they really fit this Lojban mold. -

Example 4.10, which uses the TFTT truth funct= ion, is subject to the same rules: the stated gloss of TFTT as =93only if= =94 works naturally only when the left-hand bridi is true; if it is false, = the right-hand bridi may be either true or false. The last gloss of Example 4.10 illustrates the use of =93if ... then=94 as= a more natural substitute for =93only if=94.

Example 4.10, which uses the TFTT truth funct= ion, is subject to the same rules: the stated gloss of TFTT as =93only if= =94 works naturally only when the right-hand bridi is false; if it is true,= the left-hand bridi may be either true or false. The last gloss of Example 4.10 illustrates the use of =93if ... then=94 as= a more natural substitute for =93only if=94.

 4.10)  la djan. nanmu .inaja la djeimyz. ni=
nmu
        John is-not-a-man or James is-a-woman.
        John is a man only if James is a woman.
        If John is a man, then James is a woman.

The following example illustrates the use of =93se=94 to, in effect, ex= change the two sentences. The normal use of =93se=94 is to (in effect) tran= pose places of a bridi, as explained in Chapter 5.

The following example illustrates the use of =93se=94 to, in effect, ex= change the two sentences. The normal use of =93se=94 is to (in effect) tran= spose places of a bridi, as explained in Chapter 5.

 4.11)  la djan. nanmu .iseju la djeimyz. ni=
nmu
        Whether or not John is a man, James is a woman.

If both =93na=94 and =93se=94 are present, which is legal but never necess= ary, =93na=94 would come before =93se=94.

The full syntax of ijeks, therefore, is:

        .i [na] [se] JA [nai]

where the cmavo in brackets are optional. diff --git a/14/5/index.html b/14/5/index.html index 3011964..8d271eb 100644 --- a/14/5/index.html +++ b/14/5/index.html @@ -27,22 +27,22 @@

5. Forethought bridi connection

Many concepts in Lojban are expressible in two different ways, generall= y referred to as =93afterthought=94 and =93forethought=94. Section 4 discussed what is called =93afterthought bridi logical conn= ection=94. The word =93afterthought=94 is used because the connective cmavo= and the second bridi were added, as it were, afterwards and without changi= ng the form of the first bridi. This form might be used by someone who make= s a statement and then wishes to add or qualify that statement after it has= been completed. Thus,

 5.1)   la djan. nanmu

is a complete bridi, and adding an afterthought connection to make

 5.2)   la djan. nanmu .ija la djeimyz. ninmu
        John is a man or James is a woman (or both)

-provides additional information without requiring any change in the form o= f what has come before, which may not be possible or practical, especially = in speaking. (The meaning, however, may be changed by the use of a negating= connective.) Afterthought connectives make it possible to construct all th= e important truth-functional relationships in a variety of ways. -

In forethought style the speaker decides in advance, before expressing = the first bridi, that a logical connection will be expressed. Forethought a= nd afterthought connectives are expressed with separate selma'o: the foreth= ought logical connectives corresponding to afterthought ijeks are geks:

+provides additional information without requiring any change in the form o= f what has come before; changes which may not be possible or practical, esp= ecially in speaking. (The meaning, however, may be changed by the use of a = negating connective.) Afterthought connectives make it possible to construc= t all the important truth-functional relationships in a variety of ways. +

In forethought style the speaker decides in advance, before expressing = the first bridi, that a logical connection will be expressed. Forethought a= nd afterthought connectives are expressed with separate selma'o. The foret= hought logical connectives corresponding to afterthought ijeks are geks:

 5.3)   ga la djan. nanmu gi la djeimyz. ninmu
        Either John is a man or James is a woman (or both).

=93ga=94 is the cmavo which represents the A tr= uth function in selma'o GA. The word =93gi=94 does not belong to GA at all,= but constitutes its own selma'o: it serves only to separate the two bridi = without having any content of its own. The English translation of =93ga ...= gi=94 is =93either ... or=94, but in the English form the truth function i= s specified both by the word =93either=94 and by the word =93or=94: not so = in Lojban.

Even though two bridi are being connected, geks and giks do not have an= y =93.i=94 in them. The forethought construct binds up the two bridi into a= single sentence as far as the grammar is concerned.

Some more examples of forethought bridi connection are:

 5.4)   ge la djan. nanmu gi la djeimyz. ninmu
        (It is true that) both John is a man and James is a woman.
diff --git a/14/8/index.html b/14/8/index.html
index 670b6b4..dff5103 100644
--- a/14/8/index.html
+++ b/14/8/index.html
@@ -50,21 +50,21 @@ where the semantics tells us that the instances of =93a=
nd=94 are meant to have h
        I kiss you and you kiss me, if I love you and you love me.

marking two of the ijeks with =93bo=94 for high precedence. (The first =93= bo=94 is not strictly necessary, because of the left-grouping rule, and is = shown here in brackets.)

But it may be clearer to use explicit parenthesis words and say:

 8.6)   tu'e mi cinba do .ije do cinba mi tu'u
             .ijanai tu'e mi prami do .ije do prami mi [tu'u]
        ( I kiss you and you kiss me )
             if ( I love you and you love me ).

-where the =93tu'e ... tu'u=94 pairs set off the structure. The cmavo =93tu= 'u=94 is an elidable terminator, and its second occurrence in Example 8.6 is bracketed, because all terminators may be elided= at the end of text. +where the =93tu'e ... tu'u=94 pairs set off the structure. The cmavo =93tu= 'u=94 is an elidable terminator, and its second occurrence in Example 8.6 is bracketed, because all terminators may be elided= at the end of a text.

In addition, parentheses are a general solution: multiple parentheses m= ay be nested inside one another, and additional afterthought material may b= e added without upsetting the existing structure. Neither of these two adva= ntages apply to =93bo=94 grouping. In general, afterthought constructions t= rade generality for simplicity.

Because of the left-grouping rule, the first set of =93tu'e ... tu'u=94= parentheses may actually be left off altogether, producing:

 8.7)   mi cinba do .ije do cinba mi
             .ijanai tu'e mi prami do .ije do prami mi [tu'u]
        I kiss you and you kiss me
             if ( I love you and you love me ).

What about parenthesized sumti connection? Consider

diff --git a/14/9/index.html b/14/9/index.html
index 6b2c0be..ec04008 100644
--- a/14/9/index.html
+++ b/14/9/index.html
@@ -72,21 +72,21 @@ where the double =93vau=94 at the end of Example 9.8 term
  9.9)   klama le zarci gi'e dzukla le briju
        A goer to-the market and a walker to-the office.
 
 Since x1 is omitted in both of the bridi underlying E=
xample 9.9, this compound bridi does not necessarily imply that the goe=
r and the walker are the same. Only the presence of an explicit x1 (other t=
han =93zo'e=94, which is equivalent to omission) can force the goer and the=
 walker to be identical.
 A strong argument for this convention is provided by analysis of the fo=
llowing example:
  9.10)  klama la nu,IORK. la finyks. gi'e kl=
ama la nu,IORK. la rom.
        A goer to-New York from-Phoenix and a goer to-New York from-Rome.
 
-If the rule were that the x1 places of the two underlying bridi were ident=
ical, then (since there is nothing special about x1), the unspecified x4 (r=
oute) and x5 (means) places would also have to be the same, leading to the =
absurd result that the route from Phoenix to New York is the same as the ro=
ute from Rome to New York. Inserting =93da=94, meaning roughly =93something=
=94, into the x1 place cures the problem:
+If the rule were that the x1 places of the two underlying bridi were consi=
dered identical, then (since there is nothing special about x1), the unspec=
ified x4 (route) and x5 (means) places would also have to be the same, lead=
ing to the absurd result that the route from Phoenix to New York is the sam=
e as the route from Rome to New York. Inserting =93da=94, meaning roughly =
=93something=94, into the x1 place cures the problem:
  9.11)  da klama la nu,IORK. la finyks.
             gi'e klama la nu,IORK. la rom.
        Something is-a-goer to-New York from-Phoenix
            and is-a-goer to-New York from-Rome.
 
 The syntax of giheks is:
        [na] [se] GIhA [nai]
 

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Chapter 14
If Wishes Were Horses: The Lojban Connective System

1. Logical connection and truth tables

13. Truth questions and connective questions

18. Tenses, modals, and logical connection

20. Constructs and appropriate connectives

21. Truth functions and corresponding logical connectives

22. Rules for making logical and non-logical connectives

5. Forethought bridi connection

Chapter 14 If Wishes Were Horses: The Lojban Connective System

1. Logical connection and truth tables

13. Truth questions and connective questions

18. Tenses, modals, and logical connection

20. Constructs and appropriate connectives

21. Truth functions and corresponding logical connectives

22. Rules for making logical and non-logical connectives

5. Forethought bridi connection

Chapter 14
If Wishes Were Horses: The Lojban Connective System