Bongard Problems sorted left have the keyword "precise" on the OEBP.

Bongard Problems sorted right have the keyword "fuzzy" on the OEBP.

In an precise Bongard Problem, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted.

(All relevant examples clearly sorted either left or right is the keyword allsorted.)

How can it be decided whether or not a rule is precise? How can it be decided whether or not a rule classifies all "examples that are relevant"? There needs to be another rule to determine which examples the original rule intends to sort. Bongard Problems by design communicate ideas without fixing that context ahead of time. The label "precise" can only mean a Bongard Problem's rule seems precise to people who see it. (This "precise vs. fuzzy" Bongard Problem is fuzzy.)

In an precise "less than ___ vs. greater than ___" Bongard Problem (keyword spectrum), the division between the sides is usually an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles (see e.g. BP292).

As a rule of thumb, do not consider imperfections of hand drawn images (keyword ignoreimperfections) when deciding whether a Bongard Problem is precise or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be labelled fuzzy; similar vagueness arises in all hand-drawn Bongard Problems. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword perfect.)

Sometimes the way a Bongard Problem would sort certain examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a precise criterion that has been used to verify each sorted example fits where it fits (some kind of mathematical proof); however, where some examples fit is still unknown. Whether or not such a Bongard Problem should be labelled "precise" might be debated.

(Technical note: some properties are known to be undecidable, and sometimes the decidability itself is unknown. See https://en.wikipedia.org/wiki/Decision_problem .)

(See the keyword proofsrequired.)

One way to resolve this ambiguity is to define "precise" as meaning that once people decide where an example belongs for a reason, they will all agree about it.

Sometimes the class of all examples in a Bongard Problem is imprecise, but, despite that, the rule sorting those examples is precise. Say, for some potential new example, it is unclear whether it should be included in the Bongard Problem at all, but, if it were included, it would be clear where it should be sorted (or that it should be left unsorted). A Bongard Problem like this can still be tagged "precise".

(If all examples are clearly sorted except for some example for which it is unclear whether it belongs to the class of relevant examples, the situation becomes ambiguous.)

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword preciseworld.)

There is a subtle distinction to draw between Bongard Problems that are precise to the people making them and Bongard Problems that are precise to the people solving them. A Bongard Problem (particularly a non-allsorted one) might be labeled "precise" on the OEBP because the description and the listed ambiguous examples explicitly forbid sorting certain border cases; however, someone looking at the Bongard Problem without access to the OEBP page containing the definition would not be aware of this. It may or may not be obvious that certain examples were intentionally left out of the Bongard Problem. A larger collection of examples may make it more clear that a particularly blatant potential border case was left out intentionally.

See BP876 for the version with pictures of Bongard Problems instead of links to pages on the OEBP.

See both and neither for specific ways an example can be classified as unsorted in an "precise" Bongard Problem.

Adjacent-numbered pages:
BP503 BP504 BP505 BP506 BP507  *  BP509 BP510 BP511 BP512 BP513

fuzzy, meta (see left/right), links, keyword, right-self, sideless

bp [smaller | same | bigger]

Aaron David Fairbanks

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

Call a rule "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow rule. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow rule seems small in comparison to the space of other related possibilities. Narrow rules tend to be phrased positively ("is [property]"), while non-narrow rules opposite narrow rules tend to be phrased negatively ("is not [property]").

Both sides of a BP can be narrow, e.g. BP6.

Even a rule and its conceptual opposite can be narrow, e.g. BP20.

What seems like a typical example depends on expectations. If one is expecting there to be triangles, the absence of triangles will be noticeable. (See the keyword assumesfamiliarity for Bongard Problems that require the solver to go in with special expectations.)

A person might notice the absence of triangles in a collection of just polygons, because a triangle is such a typical example of a polygon. On the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

Typically, any example fitting a narrow rule can be changed slightly to no longer fit. (This is not always the case, however. Consider the narrow rule "is approximately a triangle".)

It is possible for a rule to be "narrow" (communicable by a properly chosen collection of examples) but not clearly communicated by a particular collection of examples satisfying it, e.g., a collection of examples that is too small to communicate it.

Note that this is not just BP514 (right-narrow) flipped.

Is it possible for a rule to be such that some collections of examples do bring it to mind, but no collection of examples unambiguously communicates it as the intended rule? Perhaps there is some border case the rule excludes, but it is not clear whether the border case was intentionally left out. The border case's absence would likely become more conspicuous with more examples (assuming the collection of examples naturally brings this border case to mind).

See BP830 for a version with pictures of Bongard Problems (miniproblems) instead of links.

Adjacent-numbered pages:
BP508 BP509 BP510 BP511 BP512  *  BP514 BP515 BP516 BP517 BP518

dual, meta (see left/right), links, keyword, side

bp [smaller | same | bigger]

Aaron David Fairbanks

Left-sorted Bongard Problems have the the keyword "right-narrow" on the OEBP.

This sorts Bongard Problems based on how BP513 (left-narrow) would sort them if they were flipped; see that page for a description.

Adjacent-numbered pages:
BP509 BP510 BP511 BP512 BP513  *  BP515 BP516 BP517 BP518 BP519

dual, meta (see left/right), links, keyword, side

bp [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP583 BP584 BP585 BP586 BP587  *  BP589 BP590 BP591 BP592 BP593

meta (see left/right), links, metaconcept, primitive

bp [smaller | same | bigger]

Harry E. Foundalis

Adjacent-numbered pages:
BP656 BP657 BP658 BP659 BP660  *  BP662 BP663 BP664 BP665 BP666

meta (see left/right), links, metaconcept, primitive

bp [smaller | same | bigger]

Harry E. Foundalis

Adjacent-numbered pages:
BP1018 BP1019 BP1020 BP1021 BP1022  *  BP1024 BP1025 BP1026 BP1027 BP1028

meta (see left/right), links, metaconcept

bp [smaller | same | bigger]

Aaron David Fairbanks

This classification is specifically concerned with changes to examples that leave them sortable, as there are almost always ways of adding details to a BP's examples that make them unsortable.

Right-sorted BPs in this Bongard Problem are often Bongard Problems where there is always a way of adding to left-sorted examples to make them right-sorted, but not the other way around, or vice versa.

Another version of this Bongard Problem could be made about adding white (erasure of detail) instead of black (addition of detail).

Another version could be made about adding either white or black, but not both.

Where appropriate, you can assume all images will have some room in a lip of white background around the border (ignoring https://en.wikipedia.org/wiki/Sorites_paradox ).

You can't expand the boundary of an image as you add detail to it. If image boundaries could be expanded, then any shape could be shrunken to a point in relation to the surrounding whiteness, which could then be filled in to make any other shape.

How should this treat cases in which just a few examples can't be added to at all (like an all-black box)? E.g. BP966. Should this be sorted right (should the one special case of a black box spoil it) or should it be sorted left (should examples that can't at all be further added be discounted)? Maybe we should only sort BPs in which all examples can be further added to. (See BP1143^left.) - Aaron David Fairbanks, Nov 12 2021

Is "addition of detail" context-dependent, or does it just mean any addition of blackness to the image? Say you have a points-and-lines Bongard Problem like BP1100, and you're trying to decide whether to sort it left or right here. You would just want to think about adding more points and lines to the picture. You don't want to get bogged down in thinking about whether black could be added to the image in a weird way so that a point gets turned into a line, or something. - Aaron David Fairbanks, Nov 13 2021

See BP1139 for Bongard Problems in which no example can be added to, period.

Adjacent-numbered pages:
BP1134 BP1135 BP1136 BP1137 BP1138  *  BP1140 BP1141 BP1142 BP1143 BP1144

meta (see left/right), links, sideless

Leo Crabbe

Left-sorted Bongard Problems have the keyword "both" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side (keyword neither) rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword allsorted.)

"Is a rhombus" and "is a rectangle" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords left-narrow and right-narrow for more explanation.)

The keywords both and allsorted are mutually exclusive.

Adjacent-numbered pages:
BP1183 BP1184 BP1185 BP1186 BP1187  *  BP1189 BP1190 BP1191 BP1192 BP1193

meta (see left/right), links, keyword

Aaron David Fairbanks

Left-sorted Bongard Problems are tagged with the keyword "preciseworld" on the OEBP.

The keyword "preciseworld" basically means: if a new Bongard Problem were created to sort whether or not examples fit in the pool of examples in the original Bongard Problem, it would be tagged precise.

For a Bongard Problem fitting left, the intended class of examples sorted by the Bongard Problem is clear-cut.

For a Bongard Problem fitting right, there isn't any obvious boundary to take as delimiting the pool of potential examples. There is an imprecise fading of relevancy rather than a natural cutoff point.

Sometimes there are specific notable cases of potential examples for which there is ambiguity about whether they belong.

For example, the empty square (zero dots) has been left out of BP989. This is perhaps the only obvious example that is ambiguous as to whether it should be considered as belonging to the pool of examples shown in the Bongard Problem (or any similar dot-counting Bongard Problem).

(There would be no ambiguity if it were actually included in the Bongard Problem.)

(Whether or not zero seems like an obvious example also has a cultural component (see culture); someone who is not accustomed think of zero as a number might not see this as ambiguous at all.)

Larger pools of examples make the absence of notable border cases like this more conspicuous and intentional-seeming. (See also discussion at left-narrow.) But expanding the pool of examples cannot resolve certain border cases: if the rule of the Bongard Problem by nature leaves unsorted a potential example that is a border case for even fitting in with the rest of the examples, its absence doesn't communicate anything; whether it belongs with the pool of examples remains ambiguous.

It is tempting to make another another "allsortedworld" analogous to allsorted. But the pool of relevant examples fitting in a Bongard Problem is like a Bongard Problem with only one side: a collection satisfying some rule. Would there be any difference between precise and allsorted for a Bongard Problem with only one side?

Adjacent-numbered pages:
BP1185 BP1186 BP1187 BP1188 BP1189  *  BP1191 BP1192 BP1193 BP1194 BP1195

Bongard Problems featuring generic shapes ( https://oebp.org/search.php?q=world:fill_shape ) have not usually been labelled "preciseworld". (What counts as a "shape"? Can the shapes be fractally complicated, for example? What exactly are the criteria?) Nonetheless, these Bongard Problems are frequently precise.

meta (see left/right), links, keyword

Aaron David Fairbanks

Adjacent-numbered pages:
BP1230 BP1231 BP1232 BP1233 BP1234  *  BP1236 BP1237 BP1238 BP1239 BP1240

meta (see left/right), metaconcept

bp [smaller | same | bigger]

Aaron David Fairbanks