Left-sorted Problems have the keyword "left-listable" on the OEBP.

All the possible left examples for the BPs on the left side of this problem could be listed in one infinite sequence. Right examples here are Problems for which no such sequence can exist.

This depends on deciding what images should be considered "the same thing", which is subjective and context-dependent.

All examples in this Bongard Problem have an infinite left side (they do not have the keyword left-finite).

The mathematical term for a set that can be organized into an infinite list is a "countably infinite" set, as opposed to an "uncountably infinite" set.

Another related idea is a "recursively enumerable" a.k.a. "semi-decidable" set, which is a set that a computer program could list the members of.

The keyword "left-listable" is meant to be for the more general idea of a countable set, which does not have to do with computer algorithms.

Note that this is not just BP940 (right-listable) flipped.

It seems in practice, Bongard Problems that are left-listable are usually also right-listable because the whole class of relevant examples is listable. A keyword for just plain "listable" may be more useful. Or instead keywords for left- versus right- semidecidability, in the sense of computing. - Aaron David Fairbanks, Jan 10 2023

https://en.wikipedia.org/wiki/Countable_set

See left-finite, which distinguishes between a finite left side and infinite left side.

"Left-listable" BPs are typically precise.

Adjacent-numbered pages:
BP558 BP559 BP560 BP561 BP562  *  BP564 BP565 BP566 BP567 BP568

math, meta (see left/right), links, keyword

bp_infinite_left_examples [smaller | same | bigger]
zoom in right (left_uncountable_bp)

Leo Crabbe

Left examples have the keyword "overriddensolution" on the OEBP.

An "overriddensolution" is solution idea for a Bongard Problem that would not be chosen by the solver because there is a simpler solution that always comes with it.

An overridden solution occurs when the Bongard Problem's examples on both sides all share some constraint, and furthermore within this constrained class of examples, the intended rule is equivalent to a simpler rule that can be understood without noticing the constraint. See e.g. BP1146. The solver of the Bongard Problem will get the solution before noticing the constraint.

There is a more extreme class of overridden solution: not only is the solution possible to overlook in favor of something simpler, but even with scrutiny it will likely never be recognized. See e.g. BP570. This happens when intended left and right side rules are not direct negations of one another, but one or both of these rules is not "narrow"-- it can only be communicated in a Bongard Problem by its opposite being on the other side.

TO DO: Should this more extreme version have its own keyword? - Aaron David Fairbanks, Nov 23 2021

The keyword left-narrow (resp. right-narrow) is for Bongard Problems whose left-side (resp. right-side) rule can be recognized alone without examples on the other side.

The keyword notso is for Bongard Problems whose two sides are direct negations of one another.

See keyword impossible for solution ideas that cannot even apply to any set of examples, much less be communicated as the best solution.

Adjacent-numbered pages:
BP563 BP564 BP565 BP566 BP567  *  BP569 BP570 BP571 BP572 BP573

BP570 "Shape outlines that aren't triangles vs. black shapes that aren't squares" was created as an example of this.

meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks