# utka fu'ivla

x1 and x2 are path-linked by binary predicate x3 (ka) via intermediate steps x4 (ce'o; (ordered) list).

For example, "lo stedu ku utka lo birka lo ka (ce'u ce'u) lamji" is true, with x4 equal to something like "lo cnebo ce'o lo cutne ce'o lo janco". (Also: "lo stedu ku lamji'utka lo birka".) Formally, "utka(A,B,P,[L1, ..., L" is equivalent to "P(A,L1) and P(L1, L and ... and P(L(n-1),L and P(Ln,B)". The x4 may be empty ("lo nomei") if there are no intermediate steps (id est: the relevant path-linking between x1 and x2 is direct). x4 is a list of only the intermediate steps between x1 and x2 and does not include x1 or x2 themselves; it is ordered so that the relevant relation (x3) holds between x1 and the first term/entry of the list (in that order), between each successive pair of consecutive terms/entries of the list (in the order in which they are listed), and between the last term/entry of the list and x2 (in that order). x4 may not be unique. x3 may not be symmetric (commutative) under exchange of its operands. The predicate may be asymmetrical (thus, graph-theoretically, the edges may be directed). Neither acyclicity nor geodesicity is implied. At the level of conceptual resolution being employed in the context of its usage, x4 should specify every node along at least one path from x1 to x2 in order and without any gaps/omissions. See also: ".efku", "ki'irsi", ".utka'au", "takni", "taknyklojyzilpra". See ".utkaro" and ".utkakpu" for somewhat stronger conditions, and ".utkaje" for a stronger condition still; see ".utkazo" for a weaker condition than this word (namely: allowing omissions in the path specification), and ".utkazau" for an alternative.

## In notes:

jatny'utka
x1 is the captain/commander/leader/boss/superior of/to the captain/commander/leader/boss/superior of/to the captain/commander/leader/boss/superior of/to the ... captain/commander/leader/boss/superior of/to x2 (subject, entity, vehicle, domain), connected by intermediate steps x3.
jorny'utka
x1 is joined/connected to/with something which is joined/connected to/with something which ... which is joined/connected to/with something which is joined/connected to/with x2 via intermediate things/steps x3 (ce'o), with respective points/loci of (con)juncture x4 (ce'o).
mindy'utka
x1 directly or indirectly commands x2, via intermediaries x3 (ce'o; ordered list), for result x4 (event) to occur.
pafy'utka
x1 is patrilineal/agnatic to/an agnate of x2; x1 is path-connected to x2 via the fatherhood relation, connected by a graph-path passing through intermediate relations/steps (successive agnates) x3 (ce'o; ordered list).
pavmompazy'utka'au'ypanzi
x1 is any child of the first child of the first child of ... the first child of x2, where the graph geodesic through the ancestorship-directed family tree from x1 to x2 is of length (x3) + 1 (li; x3 must be a nonnegative integer or positive infinity), and where "first" is according to (partial) ordering rule x4 (default: chronological order of birth per successive generation within the given lineage; other restrictions on legitimacy etc. may be specified here as well).
pedy'utka
x1 is a friend of a friend of ... a friend of x2 (experiencer), path-connected by the directed friendship relationship via intermediate nodes (friends) x3 (list; ce'o).
pendy'utka
x1 is a friend of a friend of ... a friend of x2 (experiencer), path-connected by the directed friendship relationship via intermediate nodes (friends) x3 (list; ce'o).
prejumydu'a'y'utka
x1 infects a recipient who infects a recipient who infects ... who infects recipient x2 with contagion x3 via means of infection/contamination x4 and through intermediaries x5 (ce'o list).; x1 spreads contagion x3 through a network such that they indirectly infect x2 via a route through finitely-many intermediary nodes x5.
selprejumydu'a'y'utka
x1 is infected/contaminated by something which was infected/contaminated by something which was infected/contaminated by ... which was infected/contaminated by x2, regarding/pertaining to contagion x3 and via means of transmission x4, through intermediary nodes x5 (ce'o list).
selterselcple'ijdy'utka
x1 gives/pays x2 to someone who gives pays (some portion of) x2 or the equivalent thereof (possibly united with other things) to someone who gives/pays ... to someone who gives/pays (some portion of) their relevant gift/payment or the equivalent thereof (possibly united with other things/payment) to x3 through intermediate steps x4 (ce'o).
sity'utka
x1 = sitna1 = utka1 cites/quotes/refers to/makes reference to a source, which itself/who themself cites/quotes/refers to/makes reference to a source, which itself/who themself in turn cites/quotes/refers to/makes reference to source, ..., which itself/who themself cites/quotes/refers to/makes reference to source x2 = sitna2 = utka2, via intermediate path-connecting steps x3 = utka3 (ordered list; ce'o), all for the same information/statement x4 = sitna3 (du'u).
dunliki
Something is such that both x1 and x2 are related to it by predicate x3. x4 [quantifier] thing to which x1 is related by predicate x3 is such that x2 is related to it by predicate x3.
lamji'utka
x1 is directly or indirectly touching x2 via intermediate steps x3 (ce'o list); x1 and x2 belong to the same connected component.
treicu
x1 is a (general(ized)) heirarchical/pyramidal/directed tree-graph structure on underlying set x2 via partial ordering relation x3 (see notes for default properties).
utka'au
x1 and x2 are path-linked by binary predicate x3 (ka; possibly non-symmetric/non-commutative) via a from-x1-to-x2-directed graph geodesic of length x4 (li; nonnegative integer or positive infinity) in graph x5 (default: maximal) which is generated by relation x3.
.utkakpu
x1 and x2 are path-connected by ordered binary relation/predicate x3 (ka), such that all paths which satisfy condition(s) x4 (ka; default: no additional conditions) in the relevant graph (x5) linking nodes by said relation x3 in a directed manner and which contain x1 must also (later in the path) contain x2.
utkakpu
x1 and x2 are path-connected by ordered binary relation/predicate x3 (ka), such that all paths which satisfy condition(s) x4 (ka; default: no additional conditions) in the relevant graph (x5) linking nodes by said relation x3 in a directed manner and which contain x1 must also (later in the path) contain x2.
utkaro
x1 and x2 are path-linked by directed binary predicate x3 (ka) via intermediate steps x4 (ordered list; ce'o), such that no other node exists in the graph (x5) to which x2 is connected in the same way/direction as x1 is (possibly-indirectly) connected to x2 via x3 (id est: as being such that x2 is the first argument of the x3 and the hypothetical other node is the second argument thereof).
utkazau
x1 is linked by binary predicate x2 (ka) to x3. which in turn is linked by x2 to x4, which in turn is linked by x2 to x5, ...
utkazo
x1 and x2 are path-linked by binary predicate x3 (ka) via intermediate steps x4 (ce'o; (ordered) list but not necessarily fully and explicitly specified without skipping/gaps/omissions/implicit terms).
ve'irsau'utka
x1 is remembered by someone/something which remembers ... which remembers someone/something which is remembered by x2 via intermediate nodes/steps x3 (ce'o; ordered list).