## 14.14. Non-logical connectives

Way back in Section 14.1, the point was made that not every use of English and, if ... then, and so on represents a Lojban logical connective. In particular, consider the and of:

Example 14.109.

John and Alice carried the piano.

Given the nature of pianos, this probably means that John carried one end and Alice the other. So it is not true that:

Example 14.110.

John carried the piano, and Alice carried the piano.

which would mean that each of them carried the piano by himself/herself. Lojban deals with this particular linguistic phenomenon as a mass. John and Alice are joined together into a mass, John-and-Alice, and it is this mass which carried the piano, not either of them separately. The cmavo joi (of selma'o JOI) is used to join two or more components into a mass:

Example 14.111.

 la djan. joi la .alis. cu bevri le pipno That-named John massed-with that-named Alice carry the piano.

Example 14.111 covers the case mentioned, where John and Alice divide the labor; it also could mean that John did all the hauling and Alice did the supervising. This possibility arises because the properties of a mass are the properties of its components, which can lead to apparent contradictions: if John is small and Alice is large, then John-and-Alice is both small and large. Masses are also discussed in Section 6.3.

Grammatically, joi can appear between two sumti (like an ek) or between two tanru components (like a jek). This flexibility must be paid for in the form of occasional terminators that cannot be elided:

Example 14.112.

 le nanmu ku joi le ninmu [ku] cu klama le zarci The man massed-with the woman go-to the market.

The cmavo ku is the elidable terminator for le, which can almost always be elided, but not in this case. If the first ku were elided here, Lojban's parsing rules would see le nanmu joi and assume that another tanru component is to follow; since the second le cannot be part of a tanru, a parsing error results. No such problem can occur with logical connectives, because an ek signals a following sumti and a jek a following tanru component unambiguously.

Single or compound cmavo involving members of selma'o JOI are called joiks, by analogy with the names for logical connectives. It is not grammatical to use joiks to connect bridi-tails.

In tanru, joi has the connotation mixed with, as in the following example:

Example 14.113.

 ti blanu joi xunre bolci This is-a-(blue mixed-with red) ball.
 This is a blue and red ball.

Here the ball is neither wholly blue nor wholly red, but partly blue and partly red. Its blue/redness is a mass property. (Just how blue something has to be to count as wholly blue is an unsettled question, though. A blanu zdani may be so even though not every part of it is blue.)

There are several other cmavo in selma'o JOI which can be used in the same grammatical constructions. Not all of them are well-defined as yet in all contexts. All have clear definitions as sumti connectives; those definitions are shown in the following table:

 A joi B the mass with components A and B A ce B the set with elements A and B A ce'o B the sequence with elements A and B in order A sece'o B the sequence with elements B and A in order A jo'u B A and B considered jointly A fa'u B A and B respectively A sefa'u B B and A respectively A jo'e B the union of sets A and B A ku'a B the intersection of sets A and B A pi'u B the cross product of sets A and B A sepi'u B the cross product of sets B and A

The cmavo se is grammatical before any JOI cmavo, but only useful with those that have inherent order. Here are some examples of joiks:

Example 14.114.

 mi cuxna la .alis. la frank. I choose that-named Alice from-that-named Frank
 ce la .alis. ce la djeimyz. and-member that-named Alice and-member that-named James.
 I choose Alice from among Frank, Alice, and James.

The x3 place of cuxna is a set from which the choice is being made. A set is an abstract object which is determined by specifying its members. Unlike those of a mass, the properties of a set are unrelated to its members' properties: the set of all rats is large (since many rats exist), but the rats themselves are small. This chapter does not attempt to explain set theory (the mathematical study of sets) in detail: explaining propositional logic is quite enough for one chapter!

In Example 14.114 we specify that set by listing the members with ce joining them.

Example 14.115.

 ti liste mi ce'o do ce'o la djan. This is-a-list-of me and-sequence you and-sequence that-named John.
 This is a list of you, me, and John.

The x2 place of liste is a sequence of the things which are mentioned in the list. (It is worth pointing out that lo liste means a physical object such as a grocery list: a purely abstract list is lo porsi, a sequence.) Here the three sumti connected by ce'o are in a definite order, not just lumped together in a set or a mass.

So joi, ce, and ce'o are parallel, in that the sumti connected are taken to be individuals, and the result is something else: a mass, a set, or a sequence respectively. The cmavo jo'u serves as a fourth element in this pattern: the sumti connected are individuals, and the result is still individuals – but inseparably so. The normal Lojban way of saying that James and George are brothers is:

Example 14.116.

 la djeimyz. bruna la djordj. That-named James is-the-brother-of that-named George.

possibly adding a discursive element meaning and vice versa. However, James and George are brothers cannot be correctly translated as:

Example 14.117.

 la djeimyz. .e la djordj. bruna That-named James and that-named George is-a-brother.

since that expands to two bridi and means that James is a brother and so is George, but not necessarily of each other. If the e is changed to jo'u, however, the meaning of Example 14.116 is preserved:

Example 14.118.

 la djeimyz. jo'u That-named James in-common-with that-named
 la djordj. cu remei bruna George are-a-twosome type-of-brothers.

The tanru remei bruna is not strictly necessary in this sentence, but is used to make clear that we are not saying that James and George are both brothers of some third person not specified. Alternatively, we could turn the tanru around: the x1 place of remei is a mass with two components, leading to:

Example 14.119.

 la djeimyz. joi That-named James massed-with
 la djordj. cu bruna remei that-named George are-a-brother type-of-twosome.

where joi is used to create the necessary mass.

Likewise, fa'u can be used to put two individuals together where order matters. Typically, there will be another fa'u somewhere else in the same bridi:

Example 14.120.

 la djeimyz. fa'u la djordj. That-named James jointly-in-order-with that-named George
 prami la meris. fa'u la martas. loves that-named Mary jointly-in-order-with that-named Martha.
 James and George love Mary and Martha, respectively.

Here the information carried by the English adverb respectively, namely that James loves Mary and George loves Martha, is divided between the two occurrences of fa'u. If both uses of fa'u were to be changed to e, we would get:

Example 14.121.

 la djeimyz. .e la djordj. prami That-named James and that-named George love
 la meris. .e la martas. that-named Mary and that-named Martha.

which can be transformed to four bridi:

Example 14.122.

 la djeimyz. prami la meris. .ije la djordj. prami That-named James loves that-named Mary, and that-named George loves
 la meris. .ije la djeimyz. prami la martas. that-named Mary, and that-named James loves that-named Martha,
 .ije la djordj. prami la martas. and that-named George loves that-named Martha.

which represents quite a different state of affairs from Example 14.120. The meaning of Example 14.120 can also be conveyed by a termset:

Example 14.123.

 la djeimyz. ce'e la meris. pe'e That-named James [plus] that-named Mary [joint]
 .e la djordj. ce'e la martas. prami and that-named George [plus] that-named Martha loves.

at the expense of re-ordering the list of names so as to make the pairs explicit. This option is not available when one of the lists is only described rather than enumerated:

Example 14.124.

 la djeimyz. fa'u la djordj. prami re mensi That-named James and-respectively that-named George love two sisters.

which conveys that James loves one sister and George the other, though we are not able to tell which of the sisters is which.