John Woldemar Cowan

“ Termset logical connectives are employed for sentences that differ in more than one sumti but not in the selbri, such as:
11.1) I go to the market from the office and to the house from the school. The Lojban version of Example 11.1 requires two termsets joined by a logical connective. A “term” is either a sumti or a sumti preceded by a tense or modal tag such as “pu” or “bai”. Afterthought termsets are formed by linking terms together by inserting the cmavo “ce'e” (of selma'o CEhE) between each of them. ”

“ Causal sentences like “If you feed the pig, then it will grow” are not logical connectives of any type, but rather need a translation using “rinka” as the selbri joining two event abstractions, thus:
5.7) le nu do cidja dunda fi le xarju cu rinka le nu ri ba banro The event-of (you food-give to the pig) causes the event-of (it will grow) . Causality is discussed in far more detail in Chapter 9.
Example 5.8 and Example 5.9 illustrates a truth function, FTTF, which needs to negate either the first or the second bridi. We already understand how to negate the first bridi:
5.8) gonai la djan. ”

“ 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 Chapter 6.
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:
14.4) le nanmu ku joi le ninmu [ku] cu klama le zarci The man massed-with the woman go-to the market. ”

“ Example 6.2 means exactly the same thing as Example 6.1: one may be rigorously transformed into the other without any change of logical meaning. This rule is true in general for every different kind of logical connection in Lojban; all of them, with one exception (see Section 12) , can always be transformed into a logical connection between sentences that expresses the same truth function.
The afterthought logical connectives between sumti are eks, which contain a connective cmavo of selma'o A. If ijeks were used in Example 6.2, the meaning would be changed:
6.3) la djan. ”

“ The full set of rules for inserting “na”, “se”, and “nai” into any connective is:
Afterthought logical connectives (eks, jeks, giheks, ijeks) :
Negate first construct: Place “na” before the connective cmavo (but after the “.i” of an ijek) . Negate second construct: Place “nai” after the connective cmavo. Exchange constructs: Place “se” before the connective cmavo (after “na” if any) . Forethought logical connectives (geks, guheks) :
Negate first construct: Place “nai” after the connective cmavo. Negate second construct: Place “nai” after the “gi”. ”

“ There exist 16 possible different truth functions. A truth table is a graphical device for specifying a truth function, making it clear what the value of the truth function is for every possible value of the component sentences. ”

“ Here are some examples of joiks:
14.6) mi cuxna la .alis. la frank. ce la .alis. ce la djeimyz. I choose Alice from Frank and-member Alice and-member 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. ”

“ But Example 12.14 means that you see one thing which is both a man and a woman simultaneously! A “nanmu je ninmu” is a manwoman, a presumably non-existent creature who is both a “nanmu” and a “ninmu”.
Truth questions and connective questions So far we have addressed only sentences which are statements. Lojban, like all human languages, needs also to deal with sentences which are questions. There are many ways of asking questions in Lojban, but some of these (like questions about quantity, tense, and emotion) are discussed in other chapters. ”

“ Mathematical operands and operators can also include tense information in their logical connectives as a result of their close parallelism with sumti and tanru components respectively:
18.14) vei ci .ebabo vo [ve'o] tadni cu zvati le kumfa ( 3 and [future] 4 ) students are-at the room. Three and, later, four students were in the room. is a simple example. There is a special grammatical rule for use when a tense applies to both of the selbri in a forethought bridi-tail connection: the entire forethought construction can just be preceded by a tense. ”

“ Therefore it is similar in meaning to Example 14.13; however, that example speaks only of the men loving the women, not vice versa.
Joiks may be combined with “bo” or with “ke” in the same way as eks and jeks; this allows grouping of non-logical connections between sumti and tanru units, in complete parallelism with logical connections:
15.6) mi joibo do ce la djan. joibo la djein. cu gunma se remei (I massed-with you) and (John massed-with Jane) are-a-mass type-of-two-set asserts that there is a set of two items each of which is a mass. ”

“ I [present] stand [exclusive] between [inclusive] Dresden and Frankfurt. I am standing between Dresden (exclusive) and Frankfurt (inclusive) . In forethought, unfortunately, the GAhOs become physically separated from the endpoints, but the same rule applies: the first GAhO refers to the first endpoint.
Logical and non-logical connectives within mekso Lojban has a separate grammar embedded within the main grammar for representing mathematical expressions (or mekso in Lojban) such as “2 + 2”. Mathematical expressions are explained fully in Chapter 18. ”

“ A final use of giheks is to combine bridi-tails used as complete sentences, the Lojban observative:
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 Example 9.9, this compound bridi does not necessarily imply that the goer and the walker are the same. Only the presence of an explicit x1 (other than “zo'e”, which is equivalent to omission) can force the goer and the walker to be identical. ”

“ This rule does not apply to “tu'e” grouping of bridi, as Example 8.6 shows.
Now we have enough facilities to handle the problem of Example 7.3: “I am German, rich, and a man — or else none of these.” The following paraphrase has the correct meaning:
8.10) [tu'e] mi dotco .ijo mi ricfu [tu'u] .ije tu'e mi dotco .ijo mi nanmu [tu'u] ( I am-German if-and-only-if I am-rich ) and (I am-German if-and-only-if I am-a-man ) . The truth table, when worked out, produces T if and only if all three component sentences are true or all three are false. ”

“ TTFT first is true if second is true. TTFF first is true whether or not second is true. TFTT first is true only if second is true. TFTF whether or not first is true, second is true. TFFT first is true if and only if second is true. TFFF first is true and second is true FTTT first and second are not both true. FTTF first or second is true, but not both. FTFT whether or not first is true, second is false. ”

“ Example 17.1 exhibits afterthought logical connection between operands:
17.1) vei ci .a vo [ve'o] prenu cu klama le zarci ( Three or four ) people go-to the market. Example 17.2 is equivalent in meaning, but uses forethought connection:
17.2) vei ga ci gi vo [ve'o] prenu cu klama le zarci ( Either 3 or 4 ) people go-to the market. Note that the mekso in Example 17.1 and Example 17.2 are being used as quantifiers. Lojban requires that any mekso other than a simple number be enclosed in “vei” and “ve'o” parentheses when used as a quantifier. ”

“ I walk to the market and at the same time talk to John. Between an ijek (or ijoik) and “bo”, as in:
18.11) mi viska pa nanmu .ijebabo mi viska pa ninmu I see a man. And [later] I see a woman. I see a man, and then I see a woman. Between an ijek (or ijoik) and “tu'e”, as in:
18.12) mi viska pa nanmu .ijebatu'e mi viska pa ninmu [tu'u] I see a man. And [later] I see a woman. I see a man, and then I see a woman. And finally, between a jek (or joik) and “bo”, as in:
18.13) mi mikce jebabo ricfu I-am-a doctor and [later] rich I am a doctor and future rich person. ”

“ There is no joik question cmavo as such; however, joiks and ijoiks may be uttered in isolation in response to a logical connective question, as in the following exchange:
15.12) do djica tu'a loi ckafi ji loi tcati You desire something-about a-mass-of coffee [what connective?] a-mass-of tea? Do you want coffee or tea? 15.13) joi Mixed-mass-and. Both as a mass (i.e, mixed together) . Ugh. (Or in Lojban: .a'unaisairo'o.) ”

“ There is a parallelism between logic and set theory that makes Example 15.1 and Example 15.2 equivalent respectively to:
15.3) lo'i ricfu ja dotco cu barda The-set-of rich-or-German-things is large. and
15.4) lo'i ricfu je dotco cu cmalu The-set-of rich-and-German-things is small. The following example uses “se remei”, which is a set (not a mass) of two elements:
15.5) la djeimyz. ce [bo] la djordj. pi'u la meris. cebo la martas. cu prami se remei James and-set George cross-product Mary and-set Martha are-lover type-of-pairs. ”