Logical Connectives

Lojban expresses logical connectives so as to unambiguously indicate logical scope (the extent of the expressions being connected), as well as to isolate various non-logical features from the logical ones (as noted above for discursives). Logical connectives may be expressed in forethought forms, in which the relationship is specified before the two terms (both ... and ...); or afterthought forms, in which the relationship is specified between the two terms (..., and ...). The form of logical connectives directly indicates their scope and the associated truth table for the two connected terms. For example, a bare vowel joins sumti (.a 'alternation', a and/or b, a OR b; .e 'conjunction', a AND b). na and nai may be used to negate connected terms (na.a 'conditional', not a OR b, if a then b; .anai 'conditional', a or not b, a if b).

The parallel structures are shown in the following abbreviated table:

 sumtisumti forethoughtsentences
OR (a and/or b).aga sumti gi sumti.i ja
AND (a and b).ege sumti gi sumti.i je
XOR (a or b, not both).onaigo sumti ginai sumti.i jonai
=> (if a then b; a only if b)na.aganai sumti gi sumti.i naja
<= (a if b; if b then a).anaiga sumti ginai sumti.i janai
 tanru tanru forethoughtcompound bridi
OR (a and/or b)jagu'a selbri gi selbrigi'a
AND (a and b)jegu'e selbri gi selbrigi'e
XOR (a or b, not both)jonaigu'o selbri ginai selbrigi'onai
=> (if a then b; a only if b)najagu'anai selbri gi selbrinagi'a
<= (a if b)janaigu'a selbri ginai selbrigi'anai

These structures are illustrated in the following; as you can see, Lojban can express quite subtle logical distinctions succinctly.

mi [cu] citkati.ata[vau]
I eat this and/or that.

mi [cu] citkati.eta[vau]
I eat this and that.

mi [cu] citkatina.ata[vau]
I eat this only if that.

mi [cu] citkati.anaita[vau]
I eat this if that.

mi [cu] citka lotitnanbajonaicidjrspageti[vau]
I eat the cake-XOR-spaghetti. (I eat something that was either cake or spaghetti -- though not both.)

mi [cu] gu'anaite zarcigivecnule toldi [vau]
 ++++ ++  
I am if-shopkeeper-of-then-seller-of the butterflies. (If I own a butterfly shop, then I sell butterflies.)

ganaimigido[cu] klama[vau]
+++++ ++   
If me, then you, go.

mi [cu] klama [vau].i jedo [cu] klama [vau]
I go and you go.

klama tu [vau]gi'ecitka ti [vau][vau]
I go to that-yonder and eat this/these.

Lojban also supports non-logical connectives, such as mixed connection and set membership (ordered/un-ordered):

I eat the blue-green-mixed-with-yellow (stuff).

le blari'o kujoile pelxu [ku][vau]
I eat the blue-green (stuff) mixed-with the yellow (stuff).

(The ku before the joi in the latter example cannot be left out due to the ambiguity resolution rules invoked in the definition of Lojban.)