def verify_t_justification(self, line):
""" Returns whether the line with the given number is a (first-order
logic) tautology """
assert line < len(self.lines)
justification = self.lines[line].justification
assert justification[0] == 'T'
assert len(justification) == 1
# Task 9.7
formula = self.lines[line].formula.propositional_skeleton()[0]
return is_propositional_tautology(formula)
def prove_tautology(tautology: Formula) -> Proof:
"""Proves the given predicate-logic tautology.
Parameters:
tautology: predicate-logic tautology to prove.
Returns:
A valid proof of the given predicate-logic tautology from the axioms
`PROPOSITIONAL_AXIOMATIC_SYSTEM_SCHEMAS` via only assumption lines
and MP lines.
"""
assert is_propositional_tautology(tautology.propositional_skeleton()[0])
def is_valid(self, assumptions: AbstractSet[Schema],
lines: Sequence[Proof.Line], line_number: int) -> bool:
"""Checks if the current line is validly justified in the context of
the specified proof.
Parameters:
assumptions: assumptions/axioms of the proof.
lines: lines of the proof.
line_number: line number of the current line in the given lines.
Returns:
``True`` if the formula justified by the current line is a
(predicate-logic) tautology, ``False`` otherwise.
"""
assert line_number < len(lines) and lines[line_number] is self
propositional_formula = self.formula.propositional_skeleton()[0]
return is_propositional_tautology(propositional_formula)
def prove_tautology(tautology: Formula) -> Proof:
"""Proves the given predicate-logic tautology.
Parameters:
tautology: predicate-logic tautology to prove.
Returns:
A valid proof of the given predicate-logic tautology from the axioms
`PROPOSITIONAL_AXIOMATIC_SYSTEM_SCHEMAS` via only assumption lines
and MP lines.
"""
assert is_propositional_tautology(tautology.propositional_skeleton()[0])
# Task 9.12
prop_tautology, translation_map = tautology.propositional_skeleton()
prop_tautology_proof = prove_propositional_tautology(prop_tautology)
return prove_from_skeleton_proof(tautology, prop_tautology_proof,
translation_map)