# kei'i KEIhI experimental cmavo

non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: X1 ^C; binary: X1 - X.

In the definition and in this note, due to parsing constraints, "-" represents set exclusion; this is typically denoted as a backslash elsewhere. Each input must be a set or similar. The definition of the binary case expands to "the set of all elements which are in X1 but not in X2". This word and operator has ordered input: 'X1 kei'i X2' is not generally equivalent to 'X2 kei'i X1'; in other words, the operator is not commutative. If unary (meaning that X1 is not explicitly specified in a hypothetical expression "X1 - X"), then X1 is taken to be some universal set O in/of the discourse (of which all other mentioned sets are subsets, at the least); in this case, the word operates as the set (absolute) complement of the explicitly mentioned set here (but not in the definition) designated as X2 for clarity (id est: the output is O - X2 = X2 ^C, where "C" denotes the set absolute complement; in other words, it is the set of all elements which may be under consideration such that they are not elements of the explicitly specified set). When binary with both X1 and X2 explicitly specified, this word/operator is the set relative complement. Somewhat analogous to logical 'NOT' (just as set intersection is analogous to logical 'AND', and set union is analogous to logical '(AND/)OR'). The preferred description/name in English is "set (theoretic) exclusion". For reference: https://en.wikipedia.org/wiki/Complement_(set_theory) .

## In notes:

jo'ei'i
nonlogical connective (and mekso operator) - symmetric difference of sets
mau'au
mekso: conversion of operator/function to operand
xa'ei'o
binary mekso operator: Let the inputs X1 and X2 be sets in the same universal set O; then the result of this operator applied to them is X1^c \cup X, where for any A \subseteq O, Ac = O \setminus A.
kleivmu
x1 (set) is the relative set complement of x2 (set) in/from/with respect to/relative to set x3 (set; default: the relevant universal set).
vendaia
x1 (set) is the unique region/part in the Venn diagram of sets x2 (set of sets; exhaustive) such that each of its (i.e.: x1's) members is a member of exactly each of the explicitly-mentioned elements of x3 (set of sets; subset of x2; exhaustive) and of no other elements of x2.