updates

Backend/venv/lib/python3.12/site-packages/nltk/sem/skolemize.py

@@ -0,0 +1,148 @@
+# Natural Language Toolkit: Semantic Interpretation
+#
+# Author: Ewan Klein <ewan@inf.ed.ac.uk>
+#
+# Copyright (C) 2001-2025 NLTK Project
+# URL: <https://www.nltk.org/>
+# For license information, see LICENSE.TXT
+
+from nltk.sem.logic import (
+    AllExpression,
+    AndExpression,
+    ApplicationExpression,
+    EqualityExpression,
+    ExistsExpression,
+    IffExpression,
+    ImpExpression,
+    NegatedExpression,
+    OrExpression,
+    VariableExpression,
+    skolem_function,
+    unique_variable,
+)
+
+
+def skolemize(expression, univ_scope=None, used_variables=None):
+    """
+    Skolemize the expression and convert to conjunctive normal form (CNF)
+    """
+    if univ_scope is None:
+        univ_scope = set()
+    if used_variables is None:
+        used_variables = set()
+
+    if isinstance(expression, AllExpression):
+        term = skolemize(
+            expression.term,
+            univ_scope | {expression.variable},
+            used_variables | {expression.variable},
+        )
+        return term.replace(
+            expression.variable,
+            VariableExpression(unique_variable(ignore=used_variables)),
+        )
+    elif isinstance(expression, AndExpression):
+        return skolemize(expression.first, univ_scope, used_variables) & skolemize(
+            expression.second, univ_scope, used_variables
+        )
+    elif isinstance(expression, OrExpression):
+        return to_cnf(
+            skolemize(expression.first, univ_scope, used_variables),
+            skolemize(expression.second, univ_scope, used_variables),
+        )
+    elif isinstance(expression, ImpExpression):
+        return to_cnf(
+            skolemize(-expression.first, univ_scope, used_variables),
+            skolemize(expression.second, univ_scope, used_variables),
+        )
+    elif isinstance(expression, IffExpression):
+        return to_cnf(
+            skolemize(-expression.first, univ_scope, used_variables),
+            skolemize(expression.second, univ_scope, used_variables),
+        ) & to_cnf(
+            skolemize(expression.first, univ_scope, used_variables),
+            skolemize(-expression.second, univ_scope, used_variables),
+        )
+    elif isinstance(expression, EqualityExpression):
+        return expression
+    elif isinstance(expression, NegatedExpression):
+        negated = expression.term
+        if isinstance(negated, AllExpression):
+            term = skolemize(
+                -negated.term, univ_scope, used_variables | {negated.variable}
+            )
+            if univ_scope:
+                return term.replace(negated.variable, skolem_function(univ_scope))
+            else:
+                skolem_constant = VariableExpression(
+                    unique_variable(ignore=used_variables)
+                )
+                return term.replace(negated.variable, skolem_constant)
+        elif isinstance(negated, AndExpression):
+            return to_cnf(
+                skolemize(-negated.first, univ_scope, used_variables),
+                skolemize(-negated.second, univ_scope, used_variables),
+            )
+        elif isinstance(negated, OrExpression):
+            return skolemize(-negated.first, univ_scope, used_variables) & skolemize(
+                -negated.second, univ_scope, used_variables
+            )
+        elif isinstance(negated, ImpExpression):
+            return skolemize(negated.first, univ_scope, used_variables) & skolemize(
+                -negated.second, univ_scope, used_variables
+            )
+        elif isinstance(negated, IffExpression):
+            return to_cnf(
+                skolemize(-negated.first, univ_scope, used_variables),
+                skolemize(-negated.second, univ_scope, used_variables),
+            ) & to_cnf(
+                skolemize(negated.first, univ_scope, used_variables),
+                skolemize(negated.second, univ_scope, used_variables),
+            )
+        elif isinstance(negated, EqualityExpression):
+            return expression
+        elif isinstance(negated, NegatedExpression):
+            return skolemize(negated.term, univ_scope, used_variables)
+        elif isinstance(negated, ExistsExpression):
+            term = skolemize(
+                -negated.term,
+                univ_scope | {negated.variable},
+                used_variables | {negated.variable},
+            )
+            return term.replace(
+                negated.variable,
+                VariableExpression(unique_variable(ignore=used_variables)),
+            )
+        elif isinstance(negated, ApplicationExpression):
+            return expression
+        else:
+            raise Exception("'%s' cannot be skolemized" % expression)
+    elif isinstance(expression, ExistsExpression):
+        term = skolemize(
+            expression.term, univ_scope, used_variables | {expression.variable}
+        )
+        if univ_scope:
+            return term.replace(expression.variable, skolem_function(univ_scope))
+        else:
+            skolem_constant = VariableExpression(unique_variable(ignore=used_variables))
+            return term.replace(expression.variable, skolem_constant)
+    elif isinstance(expression, ApplicationExpression):
+        return expression
+    else:
+        raise Exception("'%s' cannot be skolemized" % expression)
+
+
+def to_cnf(first, second):
+    """
+    Convert this split disjunction to conjunctive normal form (CNF)
+    """
+    if isinstance(first, AndExpression):
+        r_first = to_cnf(first.first, second)
+        r_second = to_cnf(first.second, second)
+        return r_first & r_second
+    elif isinstance(second, AndExpression):
+        r_first = to_cnf(first, second.first)
+        r_second = to_cnf(first, second.second)
+        return r_first & r_second
+    else:
+        return first | second