# Nullable Boolean data type¶

New in version 1.0.0.

## Indexing with NA values¶

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

Changed in version 1.0.2.

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

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

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