Chapter 11: Events, Qualities, Quantities, And Other Vague Words: On Lojban Abstraction

6. Truth-value abstraction: “jei”

The “blueness of the picture” discussed in c11-§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:

✥6.1  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

✥6.2  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:

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

✥6.3 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.