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Feature set algebra for linguistics

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Features is a simple implementation of feature set algebra in Python.

Linguistic analyses commonly use sets of binary or privative features to refer to different groups of linguistic objects: for example a group of phonemes that share some phonological features like [-consonantal, +high] or a set of morphemes that occur in context of a specific person/number combination like [-participant, GROUP]. Usually, the features are applied in a way such that only some of their combinations are valid, while others are impossible (i.e. refer to no object) – for example [+high, +low], or [-participant, +speaker].

With this package, such feature systems can be defined with a simple contingency table definition (feature matrix) and stored under a section name in a simple clear-text configuration file. Each feature system can then be loaded by its name and provides its own FeatureSet subclass that implements all comparisons and operations between its feature sets according to the given definition (compatibility, entailment, intersection, unification, etc.).

Features creates the complete lattice structure between the possible feature sets of each feature system and lets you navigate and visualize their relations using the Graphviz graph layout library.


This package runs under Python 2.7 and 3.3+, use pip to install:

$ pip install features

This will also install the concepts package from PyPI providing the Formal Concept Analysis (FCA) algorithms on which this package is based.

Features is essentially a convenience wrapper around the FCA-functionality of concepts.


Features includes some predefined feature systems that you can try out immediately. To load a feature system, pass its name to features.FeatureSystem:

>>> import features

>>> fs = features.FeatureSystem('plural')

>>> fs
<FeatureSystem('plural') of 6 atoms 22 featuresets>

The built-in feature systems are defined in the config.ini file in the package directory (usually, this will be Lib/site-packages/concepts in your Python directory).

The definition of a feature system is stored in its context object:

>>> print(fs.context)  # doctest: +ELLIPSIS
<Context object mapping 6 objects to 10 properties at 0x...>
    1s|X |  |  |X |  |X |X  |   |   |X  |
    1p|X |  |  |X |  |X |   |X  |X  |   |
    2s|  |X |X |  |  |X |X  |   |   |X  |
    2p|  |X |X |  |  |X |   |X  |X  |   |
    3s|  |X |  |X |X |  |X  |   |   |X  |
    3p|  |X |  |X |X |  |   |X  |X  |   |

>>> fs.context.objects
('1s', '1p', '2s', '2p', '3s', '3p')

('+1', '-1', '+2', '-2', '+3', '-3', '+sg', '+pl', '-sg', '-pl')

>>> fs.context.bools  # doctest: +NORMALIZE_WHITESPACE
[(True, False, False, True, False, True, True, False, False, True),
 (True, False, False, True, False, True, False, True, True, False),
 (False, True, True, False, False, True, True, False, False, True),
 (False, True, True, False, False, True, False, True, True, False),
 (False, True, False, True, True, False, True, False, False, True),
 (False, True, False, True, True, False, False, True, True, False)]

It basically provies a mapping from objects to features and vice versa. Check the documentation of concepts for further information on its full functionality.

>>> fs.context.intension(['1s', '1p'])  # common features?
('+1', '-2', '-3')

>>> fs.context.extension(['-3', '+sg'])  # common objects?
('1s', '2s')

Feature sets

All feature system contain a contradicting feature set with all features that refers to no object:

>>> fs.infimum
FeatureSet('+1 -1 +2 -2 +3 -3 +sg +pl -sg -pl')

>>> fs.infimum.concept.extent

As well as a maximally general tautological feature set with no features referring to all objects:

>>> fs.supremum

>>> fs.supremum.concept.extent
('1s', '1p', '2s', '2p', '3s', '3p')

Use the feature system to iterate over all defined feature sets in shortlex extent order:

>>> for f in fs:
...     print('%s %s' % (f, f.concept.extent))
[+1 -1 +2 -2 +3 -3 +sg +pl -sg -pl] ()
[+1 +sg] ('1s',)
[+1 +pl] ('1p',)
[+2 +sg] ('2s',)
[+2 +pl] ('2p',)
[+3 +sg] ('3s',)
[+3 +pl] ('3p',)
[+1] ('1s', '1p')
[-3 +sg] ('1s', '2s')
[-2 +sg] ('1s', '3s')
[-3 +pl] ('1p', '2p')
[-2 +pl] ('1p', '3p')
[+2] ('2s', '2p')
[-1 +sg] ('2s', '3s')
[-1 +pl] ('2p', '3p')
[+3] ('3s', '3p')
[+sg] ('1s', '2s', '3s')
[+pl] ('1p', '2p', '3p')
[-3] ('1s', '1p', '2s', '2p')
[-2] ('1s', '1p', '3s', '3p')
[-1] ('2s', '2p', '3s', '3p')
[] ('1s', '1p', '2s', '2p', '3s', '3p')

The string representations will show the smallest possible notation for each feature set by default (shortlex minimum). The full representation is also available:

>>> fs('1sg').string
'+1 +sg'

>>> fs('1sg').string_maximal
'+1 -2 -3 +sg -pl'

To use the maximal representation for __str__, put str_maximal = true into the configuration (see below).


You can call the feature system with an iterable of features to retrieve one of its feature sets:

>>> fs(['+1', '+sg'])
FeatureSet('+1 +sg')

Usually, it is more convenient to let the system extract the features from a string:

>>> fs('+1 +sg')
FeatureSet('+1 +sg')

Leading plusses can be omitted. Spaces are optional. Case, order, and duplication of features are ignored.

>>> fs('2 pl')
FeatureSet('+2 +pl')

>>> fs('SG3sg')
FeatureSet('+3 +sg')

Note that commas are not allowed inside the string.


Feature sets are singletons. The constructor is also idempotent:

>>> fs('1sg') is fs('1sg')

>>> fs(fs('1sg')) is fs('1sg')

All different possible ways to notate a feature set map to the same instance:

>>> fs('+1 -2 -3 -sg +pl') is fs('1pl')

>>> fs('+sg') is fs('-pl')

Notations are equivalent, when they refer to the same set of objects (have the same extent).


Compatibility tests:

>>> fs('+1').incompatible_with(fs('+3'))

>>> fs('sg').complement_of(fs('pl'))

>>> fs('-1').subcontrary_with(fs('-2'))

>>> fs('+1').orthogonal_to(fs('+sg'))

Set inclusion (subsumption):

>>> fs('') < fs('-3') <= fs('-3') < fs('+1') < fs('1sg')


Intersection (join, generalization, closest feature set that subsumes the given ones):

>>> fs('1sg') % fs('2sg')  # common features, or?
FeatureSet('-3 +sg')

Intersect an iterable of feature sets:

>>> fs.join([fs('+1'), fs('+2'), fs('1sg')])

Union (meet, unification, closest feature set that implies the given ones):

>>> fs('-1') ^ fs('-2')  # commbined features, and?

Unify an iterable of feature sets:

>>>[fs('+1'), fs('+sg'), fs('-3')])
FeatureSet('+1 +sg')


Immediately implied/subsumed neighbors.

>>> fs('+1').upper_neighbors
[FeatureSet('-3'), FeatureSet('-2')]

>>> fs('+1').lower_neighbors
[FeatureSet('+1 +sg'), FeatureSet('+1 +pl')]

Complete set of implied/subsumed neighbors.

>>> list(fs('+1').upset())
[FeatureSet('+1'), FeatureSet('-3'), FeatureSet('-2'), FeatureSet('')]

>>> list(fs('+1').downset())  # doctest: +NORMALIZE_WHITESPACE
 FeatureSet('+1 +sg'), FeatureSet('+1 +pl'),
 FeatureSet('+1 -1 +2 -2 +3 -3 +sg +pl -sg -pl')]


Create a graph of the feature system lattice.

>>> dot = fs.graphviz()

>>> print(dot.source)  # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
// <FeatureSystem('plural') of 6 atoms 22 featuresets>
digraph plural {
    graph [margin=0]
    edge [arrowtail=none dir=back penwidth=.5]
            f0 [label="+1 &minus;1 +2 &minus;2 +3 &minus;3 +sg +pl &minus;sg &minus;pl"]
            f1 [label="+1 +sg"]
                    f1 -> f0
            f2 [label="+1 +pl"]
                    f2 -> f0

Check the documentation of this package for details on the resulting object.


If you do not need to save your definition, you can directly create a system from an ASCII-art style table:

>>> fs = features.make_features('''
...      |+male|-male|+adult|-adult|
... man  |  X  |     |   X  |      |
... woman|     |  X  |   X  |      |
... boy  |  X  |     |      |   X  |
... girl |     |  X  |      |   X  |
... ''', str_maximal=False)

>>> fs  # doctest: +ELLIPSIS
<FeatureSystem object of 4 atoms 10 featuresets at 0x...>

>>> for f in fs:
...     print('%s %s' % (f, f.concept.extent))
[+male -male +adult -adult] ()
[+male +adult] ('man',)
[-male +adult] ('woman',)
[+male -adult] ('boy',)
[-male -adult] ('girl',)
[+adult] ('man', 'woman')
[+male] ('man', 'boy')
[-male] ('woman', 'girl')
[-adult] ('boy', 'girl')
[] ('man', 'woman', 'boy', 'girl')

Note that the strings representing the objects and features need to be disjoint and features cannot be in substring relation.

To load feature systems by name, create an INI-file with your configurations, for example:

# phonemes.ini - define distinctive features

description = Distinctive vowel place features
str_maximal = true
context =
  i|  X  |     |    |  X |     |  X  |      |  X   |
  y|  X  |     |    |  X |     |  X  |  X   |      |
  ɨ|  X  |     |    |  X |  X  |     |      |  X   |
  u|  X  |     |    |  X |  X  |     |  X   |      |
  e|     |  X  |    |  X |     |  X  |      |  X   |
  ø|     |  X  |    |  X |     |  X  |  X   |      |
  ʌ|     |  X  |    |  X |  X  |     |      |  X   |
  o|     |  X  |    |  X |  X  |     |  X   |      |
  æ|     |  X  |  X |    |     |  X  |      |  X   |
  œ|     |  X  |  X |    |     |  X  |  X   |      |
  ɑ|     |  X  |  X |    |  X  |     |      |  X   |
  ɒ|     |  X  |  X |    |  X  |     |  X   |      |

Add your config file, overriding existing sections with the same name:

>>> features.add_config('docs/phonemes.ini')

If the filename is relative, it is resolved relative to the file where the add method was called. Check the documentation of the fileconfig package for details.

Load your feature system:

>>> fs = features.FeatureSystem('vowels')

>>> fs
<FeatureSystem('vowels') of 12 atoms 55 featuresets>

Retrieve feature sets, extents and intents:

>>> print(fs('+high'))
[+high -low]

>>> print('high round = %s, %s' % fs('high round').concept.extent)
high round = y, u

>>> print('i, e, o = %s' % fs.lattice[('i', 'e', 'o')].intent)
i, e, o = -low

Logical relations between feature pairs (excluding orthogonal pairs):

>>> print(fs.context.relations())  # doctest: +NORMALIZE_WHITESPACE
+high  complement   -high
+low   complement   -low
+back  complement   -back
+round complement   -round
+high  incompatible +low
+high  implication  -low
+low   implication  -high
-high  subcontrary  -low

Advanced usage

To customize the behavior of the feature sets, override the FeatureSet attribute of FeatureSystem with your subclass:

>>> class MyFeatures(features.FeatureSystem.FeatureSet):
...     @property
...     def features(self):
...         return list(self.concept.intent)

>>> class MyFeatureSystem(features.FeatureSystem):
...     FeatureSet = MyFeatures

>>> myfs = MyFeatureSystem('small')

>>> myfs('1 -pl')
MyFeatures('+1 -pl')

>>> myfs('1 -pl').features
['+1', '-2', '-pl']

See also

  • concepts – Formal Concept Analysis with Python
  • fileconfig – Config file sections as objects
  • graphviz – Simple Python interface for Graphviz


Features is distributed under the MIT license.

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