nltk.inference package¶
Submodules¶
nltk.inference.api module¶
Interfaces and base classes for theorem provers and model builders.
Prover is a standard interface for a theorem prover which tries to prove a goal from a
list of assumptions.
ModelBuilder is a standard interface for a model builder. Given just a set of assumptions.
the model builder tries to build a model for the assumptions. Given a set of assumptions and a
goal G, the model builder tries to find a counter-model, in the sense of a model that will satisfy
the assumptions plus the negation of G.
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class
nltk.inference.api.BaseModelBuilderCommand(modelbuilder, goal=None, assumptions=None)[source]¶ Bases:
nltk.inference.api.BaseTheoremToolCommand,nltk.inference.api.ModelBuilderCommandThis class holds a
ModelBuilder, a goal, and a list of assumptions. When build_model() is called, theModelBuilderis executed with the goal and assumptions.
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class
nltk.inference.api.BaseProverCommand(prover, goal=None, assumptions=None)[source]¶ Bases:
nltk.inference.api.BaseTheoremToolCommand,nltk.inference.api.ProverCommandThis class holds a
Prover, a goal, and a list of assumptions. When prove() is called, theProveris executed with the goal and assumptions.-
decorate_proof(proof_string, simplify=True)[source]¶ Modify and return the proof string :param proof_string: str the proof to decorate :param simplify: bool simplify the proof? :return: str
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class
nltk.inference.api.BaseTheoremToolCommand(goal=None, assumptions=None)[source]¶ Bases:
nltk.inference.api.TheoremToolCommandThis class holds a goal and a list of assumptions to be used in proving or model building.
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class
nltk.inference.api.ModelBuilder[source]¶ Bases:
objectInterface for trying to build a model of set of formulas. Open formulas are assumed to be universally quantified. Both the goal and the assumptions are constrained to be formulas of
logic.Expression.
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class
nltk.inference.api.ModelBuilderCommand[source]¶ Bases:
nltk.inference.api.TheoremToolCommandThis class holds a
ModelBuilder, a goal, and a list of assumptions. When build_model() is called, theModelBuilderis executed with the goal and assumptions.
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class
nltk.inference.api.ModelBuilderCommandDecorator(modelBuilderCommand)[source]¶ Bases:
nltk.inference.api.TheoremToolCommandDecorator,nltk.inference.api.ModelBuilderCommandA base decorator for the
ModelBuilderCommandclass from which other prover command decorators can extend.
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class
nltk.inference.api.ParallelProverBuilder(prover, modelbuilder)[source]¶ Bases:
nltk.inference.api.Prover,nltk.inference.api.ModelBuilderThis class stores both a prover and a model builder and when either prove() or build_model() is called, then both theorem tools are run in parallel. Whichever finishes first, the prover or the model builder, is the result that will be used.
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class
nltk.inference.api.ParallelProverBuilderCommand(prover, modelbuilder, goal=None, assumptions=None)[source]¶ Bases:
nltk.inference.api.BaseProverCommand,nltk.inference.api.BaseModelBuilderCommandThis command stores both a prover and a model builder and when either prove() or build_model() is called, then both theorem tools are run in parallel. Whichever finishes first, the prover or the model builder, is the result that will be used.
Because the theorem prover result is the opposite of the model builder result, we will treat self._result as meaning “proof found/no model found”.
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class
nltk.inference.api.Prover[source]¶ Bases:
objectInterface for trying to prove a goal from assumptions. Both the goal and the assumptions are constrained to be formulas of
logic.Expression.
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class
nltk.inference.api.ProverCommand[source]¶ Bases:
nltk.inference.api.TheoremToolCommandThis class holds a
Prover, a goal, and a list of assumptions. When prove() is called, theProveris executed with the goal and assumptions.
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class
nltk.inference.api.ProverCommandDecorator(proverCommand)[source]¶ Bases:
nltk.inference.api.TheoremToolCommandDecorator,nltk.inference.api.ProverCommandA base decorator for the
ProverCommandclass from which other prover command decorators can extend.-
decorate_proof(proof_string, simplify=True)[source]¶ Modify and return the proof string :param proof_string: str the proof to decorate :param simplify: bool simplify the proof? :return: str
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class
nltk.inference.api.TheoremToolCommand[source]¶ Bases:
objectThis class holds a goal and a list of assumptions to be used in proving or model building.
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class
nltk.inference.api.TheoremToolCommandDecorator(command)[source]¶ Bases:
nltk.inference.api.TheoremToolCommandA base decorator for the
ProverCommandDecoratorandModelBuilderCommandDecoratorclasses from which decorators can extend.
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class
nltk.inference.api.TheoremToolThread(command, verbose, name=None)[source]¶ Bases:
threading.Thread-
result¶
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run()[source]¶ Method representing the thread’s activity.
You may override this method in a subclass. The standard run() method invokes the callable object passed to the object’s constructor as the target argument, if any, with sequential and keyword arguments taken from the args and kwargs arguments, respectively.
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nltk.inference.discourse module¶
Module for incrementally developing simple discourses, and checking for semantic ambiguity, consistency and informativeness.
Many of the ideas are based on the CURT family of programs of Blackburn and Bos (see http://homepages.inf.ed.ac.uk/jbos/comsem/book1.html).
Consistency checking is carried out by using the mace module to call the Mace4 model builder.
Informativeness checking is carried out with a call to Prover.prove() from
the inference module.
DiscourseTester is a constructor for discourses.
The basic data structure is a list of sentences, stored as self._sentences. Each sentence in the list
is assigned a “sentence ID” (sid) of the form si. For example:
s0: A boxer walks
s1: Every boxer chases a girl
Each sentence can be ambiguous between a number of readings, each of which receives a
“reading ID” (rid) of the form si -rj. For example:
s0 readings:
s0-r1: some x.(boxer(x) & walk(x))
s0-r0: some x.(boxerdog(x) & walk(x))
A “thread” is a list of readings, represented as a list of rids.
Each thread receives a “thread ID” (tid) of the form di.
For example:
d0: ['s0-r0', 's1-r0']
The set of all threads for a discourse is the Cartesian product of all the readings of the sequences of sentences.
(This is not intended to scale beyond very short discourses!) The method readings(filter=True) will only show
those threads which are consistent (taking into account any background assumptions).
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class
nltk.inference.discourse.DiscourseTester(input, reading_command=None, background=None)[source]¶ Bases:
objectCheck properties of an ongoing discourse.
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add_background(background, verbose=False)[source]¶ Add a list of background assumptions for reasoning about the discourse.
When called, this method also updates the discourse model’s set of readings and threads. :param background: Formulas which contain background information :type background: list(Expression)
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add_sentence(sentence, informchk=False, consistchk=False)[source]¶ Add a sentence to the current discourse.
Updates
self._inputandself._sentences. :param sentence: An input sentence :type sentence: str :param informchk: ifTrue, check that the result of adding the sentence is thread-informative. Updatesself._readings. :param consistchk: ifTrue, check that the result of adding the sentence is thread-consistent. Updatesself._readings.
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expand_threads(thread_id, threads=None)[source]¶ Given a thread ID, find the list of
logic.Expressionobjects corresponding to the reading IDs in that thread.Parameters: - thread_id (str) – thread ID
- threads (dict) – a mapping from thread IDs to lists of reading IDs
Returns: A list of pairs
(rid, reading)where reading is thelogic.Expressionassociated with a reading IDReturn type: list of tuple
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models(thread_id=None, show=True, verbose=False)[source]¶ Call Mace4 to build a model for each current discourse thread.
Parameters: - thread_id (str) – thread ID
- show – If
True, display the model that has been found.
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static
multiply(discourse, readings)[source]¶ Multiply every thread in
discourseby every reading inreadings.Given discourse = [[‘A’], [‘B’]], readings = [‘a’, ‘b’, ‘c’] , returns [[‘A’, ‘a’], [‘A’, ‘b’], [‘A’, ‘c’], [‘B’, ‘a’], [‘B’, ‘b’], [‘B’, ‘c’]]
Parameters: - discourse (list of lists) – the current list of readings
- readings (list(Expression)) – an additional list of readings
Return type: A list of lists
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readings(sentence=None, threaded=False, verbose=True, filter=False, show_thread_readings=False)[source]¶ Construct and show the readings of the discourse (or of a single sentence).
Parameters: - sentence (str) – test just this sentence
- threaded – if
True, print out each thread ID and the corresponding thread. - filter – if
True, only print out consistent thread IDs and threads.
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class
nltk.inference.discourse.DrtGlueReadingCommand(semtype_file=None, remove_duplicates=False, depparser=None)[source]¶
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class
nltk.inference.discourse.ReadingCommand[source]¶ Bases:
object-
combine_readings(readings)[source]¶ Parameters: readings (list(Expression)) – readings to combine Returns: one combined reading Return type: Expression
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process_thread(sentence_readings)[source]¶ This method should be used to handle dependencies between readings such as resolving anaphora.
Parameters: sentence_readings (list(Expression)) – readings to process Returns: the list of readings after processing Return type: list(Expression)
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to_fol(expression)[source]¶ Convert this expression into a First-Order Logic expression.
Parameters: expression (Expression) – an expression Returns: a FOL version of the input expression Return type: Expression
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nltk.inference.discourse.discourse_demo(reading_command=None)[source]¶ Illustrate the various methods of
DiscourseTester
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nltk.inference.discourse.drt_discourse_demo(reading_command=None)[source]¶ Illustrate the various methods of
DiscourseTester
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nltk.inference.discourse.load_fol(s)[source]¶ Temporarily duplicated from
nltk.sem.util. Convert a file of first order formulas into a list ofExpressionobjects.Parameters: s (str) – the contents of the file Returns: a list of parsed formulas. Return type: list(Expression)
nltk.inference.mace module¶
A model builder that makes use of the external ‘Mace4’ package.
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class
nltk.inference.mace.Mace(end_size=500)[source]¶ Bases:
nltk.inference.prover9.Prover9Parent,nltk.inference.api.ModelBuilder
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class
nltk.inference.mace.MaceCommand(goal=None, assumptions=None, max_models=500, model_builder=None)[source]¶ Bases:
nltk.inference.prover9.Prover9CommandParent,nltk.inference.api.BaseModelBuilderCommandA
MaceCommandspecific to theMacemodel builder. It contains a print_assumptions() method that is used to print the list of assumptions in multiple formats.-
valuation¶
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nltk.inference.nonmonotonic module¶
A module to perform nonmonotonic reasoning. The ideas and demonstrations in this module are based on “Logical Foundations of Artificial Intelligence” by Michael R. Genesereth and Nils J. Nilsson.
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class
nltk.inference.nonmonotonic.ClosedDomainProver(proverCommand)[source]¶ Bases:
nltk.inference.api.ProverCommandDecoratorThis is a prover decorator that adds domain closure assumptions before proving.
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replace_quants(ex, domain)[source]¶ - Apply the closed domain assumption to the expression
- Domain = union([e.free()|e.constants() for e in all_expressions])
- translate “exists x.P” to “(z=d1 | z=d2 | … ) & P.replace(x,z)” OR
- “P.replace(x, d1) | P.replace(x, d2) | …”
- translate “all x.P” to “P.replace(x, d1) & P.replace(x, d2) & …”
Parameters: - ex –
Expression - domain – set of {Variable}s
Returns: Expression
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class
nltk.inference.nonmonotonic.ClosedWorldProver(proverCommand)[source]¶ Bases:
nltk.inference.api.ProverCommandDecoratorThis is a prover decorator that completes predicates before proving.
If the assumptions contain “P(A)”, then “all x.(P(x) -> (x=A))” is the completion of “P”. If the assumptions contain “all x.(ostrich(x) -> bird(x))”, then “all x.(bird(x) -> ostrich(x))” is the completion of “bird”. If the assumptions don’t contain anything that are “P”, then “all x.-P(x)” is the completion of “P”.
walk(Socrates) Socrates != Bill + all x.(walk(x) -> (x=Socrates)) —————- -walk(Bill)
see(Socrates, John) see(John, Mary) Socrates != John John != Mary + all x.all y.(see(x,y) -> ((x=Socrates & y=John) | (x=John & y=Mary))) —————- -see(Socrates, Mary)
all x.(ostrich(x) -> bird(x)) bird(Tweety) -ostrich(Sam) Sam != Tweety + all x.(bird(x) -> (ostrich(x) | x=Tweety)) + all x.-ostrich(x) ——————- -bird(Sam)
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class
nltk.inference.nonmonotonic.PredHolder[source]¶ Bases:
objectThis class will be used by a dictionary that will store information about predicates to be used by the
ClosedWorldProver.The ‘signatures’ property is a list of tuples defining signatures for which the predicate is true. For instance, ‘see(john, mary)’ would be result in the signature ‘(john,mary)’ for ‘see’.
The second element of the pair is a list of pairs such that the first element of the pair is a tuple of variables and the second element is an expression of those variables that makes the predicate true. For instance, ‘all x.all y.(see(x,y) -> know(x,y))’ would result in “((x,y),(‘see(x,y)’))” for ‘know’.
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unicode_repr()¶ Return repr(self).
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class
nltk.inference.nonmonotonic.UniqueNamesProver(proverCommand)[source]¶ Bases:
nltk.inference.api.ProverCommandDecoratorThis is a prover decorator that adds unique names assumptions before proving.
nltk.inference.prover9 module¶
A theorem prover that makes use of the external ‘Prover9’ package.
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class
nltk.inference.prover9.Prover9(timeout=60)[source]¶ Bases:
nltk.inference.prover9.Prover9Parent,nltk.inference.api.Prover
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class
nltk.inference.prover9.Prover9Command(goal=None, assumptions=None, timeout=60, prover=None)[source]¶ Bases:
nltk.inference.prover9.Prover9CommandParent,nltk.inference.api.BaseProverCommandA
ProverCommandspecific to theProver9prover. It contains the a print_assumptions() method that is used to print the list of assumptions in multiple formats.
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class
nltk.inference.prover9.Prover9CommandParent[source]¶ Bases:
objectA common base class used by both
Prover9CommandandMaceCommand, which is responsible for maintaining a goal and a set of assumptions, and generating prover9-style input files from them.
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class
nltk.inference.prover9.Prover9Parent[source]¶ Bases:
objectA common class extended by both
Prover9andMace <mace.Mace>. It contains the functionality required to convert NLTK-style expressions into Prover9-style expressions.
nltk.inference.resolution module¶
Module for a resolution-based First Order theorem prover.
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class
nltk.inference.resolution.BindingDict(binding_list=None)[source]¶ Bases:
object-
unicode_repr()¶ Return repr(self).
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class
nltk.inference.resolution.Clause(data)[source]¶ Bases:
list-
isSubsetOf(other)[source]¶ Return True iff every term in ‘self’ is a term in ‘other’.
Parameters: other – ClauseReturns: bool
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is_tautology()[source]¶ Self is a tautology if it contains ground terms P and -P. The ground term, P, must be an exact match, ie, not using unification.
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replace(variable, expression)[source]¶ Replace every instance of variable with expression across every atom in the clause
Parameters: - variable –
Variable - expression –
Expression
- variable –
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substitute_bindings(bindings)[source]¶ Replace every binding
Parameters: bindings – A list of tuples mapping Variable Expressions to the Expressions to which they are bound :return:
Clause
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subsumes(other)[source]¶ Return True iff ‘self’ subsumes ‘other’, this is, if there is a substitution such that every term in ‘self’ can be unified with a term in ‘other’.
Parameters: other – ClauseReturns: bool
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unicode_repr()¶ Return repr(self).
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unify(other, bindings=None, used=None, skipped=None, debug=False)[source]¶ Attempt to unify this Clause with the other, returning a list of resulting, unified, Clauses.
Parameters: - other –
Clausewith which to unify - bindings –
BindingDictcontaining bindings that should be used
during the unification :param used: tuple of two lists of atoms. The first lists the atoms from ‘self’ that were successfully unified with atoms from ‘other’. The second lists the atoms from ‘other’ that were successfully unified with atoms from ‘self’. :param skipped: tuple of two
Clauseobjects. The first is a list of all the atoms from the ‘self’ Clause that have not been unified with anything on the path. The second is same thing for the ‘other’ Clause. :param debug: bool indicating whether debug statements should print :return: list containing all the resultingClauseobjects that could be obtained by unification- other –
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class
nltk.inference.resolution.ResolutionProver[source]¶ Bases:
nltk.inference.api.Prover-
ANSWER_KEY= 'ANSWER'¶
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class
nltk.inference.resolution.ResolutionProverCommand(goal=None, assumptions=None, prover=None)[source]¶
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nltk.inference.resolution.clausify(expression)[source]¶ Skolemize, clausify, and standardize the variables apart.
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nltk.inference.resolution.most_general_unification(a, b, bindings=None)[source]¶ Find the most general unification of the two given expressions
Parameters: - a –
Expression - b –
Expression - bindings –
BindingDicta starting set of bindings with which the unification must be consistent
Returns: a list of bindings
Raises: BindingException – if the Expressions cannot be unified
- a –
nltk.inference.tableau module¶
Module for a tableau-based First Order theorem prover.
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class
nltk.inference.tableau.Categories[source]¶ Bases:
object-
ALL= 20¶
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AND= 10¶
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APP= 4¶
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ATOM= 0¶
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D_NEG= 7¶
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EQ= 18¶
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EXISTS= 19¶
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IFF= 16¶
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IMP= 14¶
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N_ALL= 8¶
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N_AND= 15¶
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N_APP= 5¶
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N_ATOM= 2¶
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N_EQ= 6¶
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N_EXISTS= 9¶
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N_IFF= 17¶
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N_IMP= 12¶
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N_OR= 11¶
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N_PROP= 3¶
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OR= 13¶
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PROP= 1¶
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class
nltk.inference.tableau.TableauProver[source]¶ Bases:
nltk.inference.api.Prover
Module contents¶
Classes and interfaces for theorem proving and model building.