11.6. Truth-value abstraction: jei

The blueness of the picture discussed in Section 11.5 refers to the measurable amount of blue pigment (or other source of blueness), not to the degree of truth of the claim that blueness is present. That abstraction is expressed in Lojban using jei, which is closely related semantically to ni. In the simplest cases, le jei produces not a number but a truth value:

Example 11.39.

 le jei li re su'i re du li vo [kei] the truth-value-of the-number 2 + 2 = the-number 4
 the truth of 2 + 2 being 4

is equivalent to truth, and

Example 11.40.

 le jei li re su'i re du li mu [kei] the truth-value-of the-number 2 + 2 = the-number 5
 the truth of 2 + 2 being 5

is equivalent to falsehood.

However, not everything in life (or even in Lojban) is simply true or false. There are shades of gray even in truth value, and jei is Lojban's mechanism for indicating the shade of grey intended:

Example 11.41.

 mi ba jdice le jei la djordj. I [future] decide the (truth-value of that-named George
 cu zekri gasnu [kei] being-a-(crime doer) ).
 I will decide whether George is a criminal.

Example 11.41 does not imply that George is, or is not, definitely a criminal. Depending on the legal system I am using, I may make some intermediate decision. As a result, jei requires an x2 place analogous to that of ni:

x1 is the truth value of (the bridi) under epistemology x2

Abstractions using jei are the mechanism for fuzzy logic in Lojban; the jei abstraction refers to a number between 0 and 1 inclusive (as distinct from ni abstractions, which are often on open-ended scales). The detailed conventions for using jei in fuzzy-logic contexts have not yet been established.