All languages need ways to connect words, phrases and sentences. In English there are a host of words for this purpose: and, or, because, additionally, however, on the other hand ... the list seems endless, as foreign students of English know all too well. Lojban also has a wide variety of words like this, known as connectives, but it is more systematic about it. (Lojban also handles some of the functions of English conjunctions in other ways — as we saw, because and so are translated with sumti tcita, not connectives.)
There are two types of connective: logical and non-logical. Logical connectives say something about whether and in what circumstances the two things connected are true; an example is .ije. Non-logical connectives do not deal with separate truth values, but group things together to form different kinds of units; an example is joi, which we've already seen in passing, and we'll be discussing again below.
Moreover, Lojban distinguishes between the logical component of connectives, and their attitudinal content. For example, most languages have different words for and and but. Logically, they both mean the same thing. In terms of attitude, however, they are different: but contains a connotation of contrast or unexpectedness, which and does not. So Lojban translates but in two parts: .e ku'i 'and — however'. This follows the Lojban principle of keeping content and attitude separate as far as possible (e.g. .ui la djiotis. klama ti has a content element — the information that Jyoti is coming here, and an attitude element — happiness.)
In this lesson we will only look at logical connectives; non-logical connectives (with one exception) will be dealt with later, along with some other attitudinals.
In order to understand Lojban connectives, we first need to look at logical connectives in general. The types of logical connective in Lojban are based on truth tables and are explained in detail in Chapter 14 of The Complete Lojban Language. However, if you're not a logician, this can be rather confusing, so here I'll look at them in terms of Boolean operators. If you haven't a clue what a Boolean operator is, don't panic; they are very simple, and you may even have used them in an internet search without realising it. On the other hand, if you've used Boolean operators in maths or computer programming, the rest is a piece of cake. The operators we will look at here are AND, OR, EOR, IF and IFF.
We have already looked at one operator: AND. A statement with AND is true if and only if both elements are true. For example, if you do an internet search for "games AND strategy", the search engine will only come up with pages that contain both games and strategy: you will get pages on strategy games, for example, but not (ideally) on simulation games or military strategy. Similarly in Lojban
is false if Fluffy is not a rabbit, or if some rabbits are long-lived. It is only true if both sentences are true.
la flufis. ractu .ije ro ractu na'e ze'u jmive
The next type we need to look at is OR. This is not always, or even usually, the same as the English word or. English is vague about or, which sometimes means 'one or the other or both', but sometimes means 'one or the other but not both'. Compare these two sentences:
If it's cold or rainy we'll stay inside.
The winner of the competition will receive a holiday in Hawaii or the cash equivalent.
English has similar problems with the word if. Sentence (1) is unclear as to what will happen if it is neither cold nor rainy. We assume that in this case we will go out, but this is not necessarily the case. Strictly speaking, we might stay inside even if the weather is beautiful. In fact there are two potential meanings here:
IF it's cold or rainy we'll stay inside.
IFF it's cold or rainy we'll stay inside.
Just to make the difference clear, here are some examples:
means that both statements are true, i.e. Romeo and Juliet love each other.
means that one of them loves the other, and perhaps both of them do.
means that either Romeo loves Juliet (but Juliet doesn't love him) or Juliet loves Romeo (but he doesn't love her).
means that if Juliet loves Romeo, he definitely loves her, but he may love her anyway (the only outcome which is impossible is that Juliet loves Romeo but he doesn't love her).
means that if Juliet loves Romeo, he loves her, and if she doesn't love him, he doesn't love her.
The basic operators OR, AND and IFF are represented in Lojban by the vowels a, e and o.
i is not used for logical connectives, since it is already in use as a sentence separator.
u is a special case, taking the logical meaning 'whether or not' — in other words, it emphasises that the second value does not affect the truth of the sentence.
The other operators, EOR and IF, are based on these vowels combined with negatives. As we shall see below, EOR is .onai and IF is .anai.
Tip: There is some controversy in the Lojban community about whether natural language if is best expressed as a logical connective (IF, IFF), or as a sumti tcita. There are a couple of strikes against IF. One is that its logical analysis, NOT A OR B, isn't terribly obvious. Another is that IFF is often what is meant, rather than IF. Yet another is that natural language if is strongly tied up with notions of causality, precondition, or deduction — none of which is particularly emphasised by IF as a strictly logical connective. For example, logical IF will give a poor rendering of "It's not true that, if I'm rich, I'm happy" — which is decidedly not the same thing as "It's not true that I'm either not rich or happy"!
For that reason, you will see many Lojbanists avoiding IF, and instead using sumti tcita like va'o 'under conditions...', seja'e 'results from ... happening', fau 'in the event of...', or ni'i 'logically caused by...'
In the following, work out whether the logical relationship represented by the emphasised word is closer to OR, EOR, IF, or IFF.