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# Nullable Boolean data type

Note

BooleanArray is currently experimental. Its API or implementation may change without warning.

## Indexing with NA values

pandas allows indexing with `NA` values in a boolean array, which are treated as `False`.

    In [1]: s = pd.Series([1, 2, 3])

    In [2]: mask = pd.array([True, False, pd.NA], dtype="boolean")

    In [3]: s[mask]
    Out[3]:
    0    1
    dtype: int64

If you would prefer to keep the `NA` values you can manually fill them with `fillna(True)`.

    In [4]: s[mask.fillna(True)]
    Out[4]:
    0    1
    2    3
    dtype: int64

## Kleene logical operations

`arrays.BooleanArray` implements Kleene Logic (sometimes called three-value logic) for logical operations like `&` (and), `|` (or) and `^` (exclusive-or).

This table demonstrates the results for every combination. These operations are symmetrical, so flipping the left- and right-hand side makes no difference in the result.

Expression | Result
--- | ---
`True & True` | `True`
`True & False` | `False`
`True & NA` | `NA`
`False & False` | `False`
`False & NA` | `False`
`NA & NA` | `NA`
`True | True` | `True`
`True | False` | `True`
`True | NA` | `True`
`False | False` | `False`
`False | NA` | `NA`
`NA | NA` | `NA`
`True ^ True` | `False`
`True ^ False` | `True`
`True ^ NA` | `NA`
`False ^ False` | `False`
`False ^ NA` | `NA`
`NA ^ NA` | `NA`

When an `NA` is present in an operation, the output value is `NA` only if the result cannot be determined solely based on the other input. For example, `True | NA` is `True`, because both `True | True` and `True | False` are `True`. In that case, we don’t actually need to consider the value of the `NA`.

On the other hand, `True & NA` is `NA`. The result depends on whether the `NA` really is `True` or `False`, since `True & True` is `True`, but `True & False` is `False`, so we can’t determine the output.

This differs from how `np.nan` behaves in logical operations. pandas treated `np.nan` is always false in the output.

In `or`

    In [5]: pd.Series([True, False, np.nan], dtype="object") | True
    Out[5]:
    0     True
    1     True
    2    False
    dtype: bool

    In [6]: pd.Series([True, False, np.nan], dtype="boolean") | True
    Out[6]:
    0    True
    1    True
    2    True
    dtype: boolean

In `and`

    In [7]: pd.Series([True, False, np.nan], dtype="object") & True
    Out[7]:
    0     True
    1    False
    2    False
    dtype: bool

    In [8]: pd.Series([True, False, np.nan], dtype="boolean") & True
    Out[8]:
    0     True
    1    False
    2     <NA>
    dtype: boolean