View source for utka

==== valsi ====
utka
==== type ====
fu'ivla
==== creator ====
[[personal/lalxu|lalxu]]
==== time entered ====
Sun May 27 12:50:39 2018
 
== English ==
=== Definition #70722 ===
 
==== definition ====
x<sub>1</sub> and x<sub>2</sub> are path-linked by binary predicate x<sub>3</sub> (ka) via intermediate steps x<sub>4</sub> (ce'o; (ordered) list).
==== notes ====

For example, "lo stedu ku utka lo birka lo ka (ce'u ce'u) lamji" is true, with <span class="MATH"><i>x</i><sub>4</sub></span> equal to something like "lo cnebo ce'o lo cutne ce'o lo janco". (Also: "lo stedu ku [[lamji'utka|lamji'utka]] lo birka".) Formally, "utka MATH
 $(A,B,P,[L_1, ..., L_n])$
 
<span class="MATH">(<i>A</i>, <i>B</i>, <i>P</i>,[<i>L</i><sub>1</sub>,..., <i>L</i><sub>n</sub>])</span>" is equivalent to "<span class="MATH"><i>P</i>(<i>A</i>, <i>L</i><sub>1</sub>)</span> and  MATH
 $P(L_1, L_2)$
 
<span class="MATH"><i>P</i>(<i>L</i><sub>1</sub>, <i>L</i><sub>2</sub>)</span> and ... and  MATH
 $P(L_<a class="undefined" href="../dict/(n-1)?bg=1;langidarg=2">(n-1)</a>,L_n)$
 
<span class="MATH"><i>P</i>(<i>L</i><sub>(n-1)</sub>, <i>L</i><sub>n</sub>)</span> and <span class="MATH"><i>P</i>(<i>L</i><sub>n</sub>, <i>B</i>)</span>". The <span class="MATH"><i>x</i><sub>4</sub></span> may be empty ("lo [[nomei|nomei]]") if there are no intermediate steps (id est: the relevant path-linking between <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span> is direct). <span class="MATH"><i>x</i><sub>4</sub></span> is a list of only the intermediate steps between <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span> and does not include <span class="MATH"><i>x</i><sub>1</sub></span> or <span class="MATH"><i>x</i><sub>2</sub></span> themselves; it is ordered so that the relevant relation (<span class="MATH"><i>x</i><sub>3</sub></span>) holds between <span class="MATH"><i>x</i><sub>1</sub></span> 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 <span class="MATH"><i>x</i><sub>2</sub></span> (in that order). <span class="MATH"><i>x</i><sub>4</sub></span> may not be unique. <span class="MATH"><i>x</i><sub>3</sub></span> 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, <span class="MATH"><i>x</i><sub>4</sub></span> should specify every node along at least one path from <span class="MATH"><i>x</i><sub>1</sub></span> to <span class="MATH"><i>x</i><sub>2</sub></span> in order and without any gaps/omissions. See also: ".[[efku|efku]]", "[[ki'irsi|ki'irsi]]", ".[[utka'au|utka'au]]", "[[takni|takni]]", "[[taknyklojyzilpra|taknyklojyzilpra]]". See ".[[utkaro|utkaro]]" and ".[[utkakpu|utkakpu]]" for somewhat stronger conditions, and ".[[utkaje|utkaje]]" for a stronger condition still; see ".[[utkazo|utkazo]]" for a weaker condition than this word (namely: allowing omissions in the path specification), and ".[[utkazau|utkazau]]" for an alternative.

==== gloss words ====

<ul><li>[[natlang/en/path-linked nodes|path-linked nodes]]</li></ul>

==== created by ====
[[personal/lalxu|lalxu]]
==== vote information ====
3
     
==== time ====
Sat Apr 15 02:42:17 2023



<br/><font size="+1">Examples</font>
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=== Etymology ===
== lojban ==
=== Definition #70723 - Preferred ===
 
==== definition ====
x<sub>1</sub> utka x<sub>2</sub> fi x<sub>3</sub> fo x<sub>4</sub> noi porsi .ijo x<sub>1</sub> ce'o x<sub>4</sub> ce'o x<sub>2</sub> cu ki'irsi x<sub>3</sub>
==== notes ====
ckini zo [[ki'irsi|ki'irsi]] .e zo [[ko'orsi|ko'orsi]]
==== created by ====
[[personal/lalxu|lalxu]]
==== vote information ====
2
     
==== time ====
Sun May 27 12:56:05 2018



<br/><font size="+1">Examples</font>
<hr/>
<dl>
</dl>

=== Etymology ===