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

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

In an exact 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" left-BP509.)

How can it be decided whether or not a rule is exact? 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 "exact" can only mean a Bongard Problem's rule seems precise to people who see it. (This "exact vs. fuzzy" Bongard Problem is fuzzy.)

In an exact "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 exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called 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 "exact" 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 redefine "exact" as meaning that once people decide where an example belongs, 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 "exact".

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

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 "exact" Bongard Problem.

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

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

In an exact 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" left-BP509.)

How can it be decided whether or not a rule is exact? 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 "exact" can only mean a Bongard Problem's rule seems precise to people who see it. (This "exact vs. fuzzy" Bongard Problem is fuzzy.)

In an exact "less than __vs. greater than__" Bongard Problem (keyword "spectrum" left-BP507), 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" right-BP913) when deciding whether a Bongard Problem is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called 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" left-BP913.)

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 "exact" 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", left-BP1125.)

One way to resolve this ambiguity is to redefine "exact" as meaning that once people decide where an example belongs, 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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact 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" left-BP509.)

How can it be decided whether or not a rule is exact? 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 "exact" can only mean a Bongard Problem's rule seems precise to people who see it. (This "exact vs. fuzzy" Bongard Problem is fuzzy.)

In an exact "less than __vs. greater than__" Bongard Problem (keyword "spectrum" left-BP507), 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 when deciding whether a Bongard Problem is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called 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" left-BP913.)

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 "exact" 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", left-BP1125.)

One way to resolve this ambiguity is to redefine "exact" as meaning that once people decide where an example belongs, 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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact 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" left-BP509.)

How can it be decided whether or not a rule is exact? 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 "exact" can only mean a Bongard Problem's rule seems precise to people who see it. (This "exact vs. fuzzy" Bongard Problem is fuzzy.)

In an exact "less than __vs. greater than__" Bongard Problem (keyword "spectrum" left-BP507), 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 when deciding whether a Bongard Problem is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called 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 "imperfectionscanmatter" left-BP913.)

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 "exact" 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", left-BP1125.)

One way to resolve this ambiguity is to redefine "exact" as meaning that once people decide where an example belongs, 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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact 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" left-BP509.)

How can it be decided whether or not a rule is exact? 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 "exact" can only mean a Bongard Problem's rule seems precise to people who see it. (This "exact vs. fuzzy" Bongard Problem is fuzzy.)

In an exact "less than __vs. greater than__" Bongard Problem (keyword "spectrum" left-BP507), 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 when deciding whether a Bongard Problem is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called 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 "imperfectionscanmatter" left-BP913.)

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 "exact" 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 .)

One way to resolve this ambiguity is to redefine "exact" as meaning that once people decide where an example belongs, 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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact BP, 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" left-BP509.)

How can it be decided whether or not a rule is exact? 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 "exact" can only mean a Bongard Problem's rule seems precise to people who see it. (This BP "exact vs. fuzzy" is fuzzy.)

In an exact "less than __vs. greater than__" BP (keyword "spectrum" left-BP507), 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 when deciding whether a BP is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called fuzzy; similar vagueness arises in all hand-drawn BPs. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionscanmatter" left-BP913.)

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 BP should be labelled "exact" 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 .)

One way to resolve this ambiguity is to redefine "exact" as meaning that once people decide where an example belongs, 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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact BP, 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" left-BP509.)

How can it be decided whether or not a rule is exact? 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 "exact" can only mean a Bongard Problem's rule seems precise to people who see it. (This BP "exact vs. fuzzy" is fuzzy.)

In an exact "less than __vs. greater than__" BP (keyword "spectrum" left-BP507), 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 when deciding whether a BP is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called fuzzy; similar vagueness arises in all hand-drawn BPs. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionscanmatter" left-BP913.)

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 BP should be labelled "exact" 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 .)

One way to resolve this ambiguity is to redefine "exact" as meaning that once people decided where an example belonged, they would 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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact BP, 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" left-BP509.)

How can it be decided whether or not a rule is exact? 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 "exact" can only mean a Bongard Problem's rule seems precise to people who see it. (This BP "exact vs. fuzzy" is fuzzy.)

In an exact "less than __vs. greater than__" BP (keyword "spectrum" left-BP507), 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 when deciding whether a BP is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called fuzzy; similar vagueness arises in all hand-drawn BPs. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionscanmatter" left-BP913.)

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 BP should be labelled "exact" 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 .)

One way to resolve this ambiguity is to redefine "exact" as meaning that once people decided where an example belonged, they would 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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact BP, 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" left-BP509.)

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

In an exact "less than __vs. greater than__" BP (keyword "spectrum" left-BP507), 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 when deciding whether a BP is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called fuzzy; similar vagueness arises in all hand-drawn BPs. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionscanmatter" left-BP913.)

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 BP should be labelled "exact" 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 .)

One way to resolve this ambiguity is to redefine "exact" as meaning that once people decided where an example belonged, they would 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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact BP, 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" left-BP509.)

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

In an exact "less than __vs. greater than__" BP (keyword "spectrum" left-BP507), 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 when deciding whether a BP is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called fuzzy; similar vagueness arises in all hand-drawn BPs. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionscanmatter" left-BP913.)

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, it is still unknown where some examples would fit. Whether or not such a BP should be labelled "exact" 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 .)

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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

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

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

In an exact BP, 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" left-BP509.)

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

In an exact "less than __vs. greater than__" BP (keyword "spectrum" left-BP507), 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 when deciding whether a BP is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called fuzzy; similar vagueness arises in all hand-drawn BPs. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionscanmatter" left-BP913.)

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, it is still unknown where some examples would fit. Whether or not such a BP should be labelled "exact" 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 .)

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 "exact".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

A Bongard Problem will be a border case here when it's ambiguous whether to even consider certain imprecisely-sorted examples relevant.

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

See "both" (left-BP1188) and "neither" (left-BP1189) for specific ways an example can be classified as unsorted in an "exact" Bongard Problem.

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

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

In an exact BP, 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" left-BP509.)

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

In an exact "less than __vs. greater than__" BP (keyword "spectrum" left-BP507), 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 when deciding whether a BP is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called fuzzy; similar vagueness arises in all hand-drawn BPs. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionscanmatter" left-BP913.)

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, it is still unknown where some examples would fit. Whether or not such a BP should be labelled "exact" 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 .)

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 "exact". On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword "exactworld" left-BP1190.)

A Bongard Problem will be a border case here when it's ambiguous whether to even consider certain imprecisely-sorted examples relevant.

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

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

In an exact BP, 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" left-BP509.)

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

In an exact "less than __vs. greater than__" BP (keyword "spectrum" left-BP507), 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 when deciding whether a BP is exact or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be called fuzzy; similar vagueness arises in all hand-drawn BPs. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionscanmatter" left-BP913.)

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, it is still unknown where some examples would fit. Whether or not such a BP should be labelled "exact" 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 .)

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 "exact". On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. See the keyword "exactworld" (left-BP1190).

A Bongard Problem will be a border case here when it's ambiguous whether to even consider certain imprecisely-sorted examples relevant.