Tags: proof-by-refutation-2 python declaration class

ProofByRefutation2Declaration (python class)

This section presents the ProofByRefutation2Declaration python class.

This class models the declaration of the proof-by-refutation-2 inference-rule in the target universe-of-discourse.

Punctilious users do not need to instanciate objects from this class. In effect, the UniverseOfDiscourse class exposes the proof_by_refutation_2 property, and instanciation is automatic when the property is accessed for the first time.

class punctilious.ProofByRefutation2Declaration(u, echo=None)

This python class models the inclusion of proof-by-refutation-2 as a valid inference-rule in a theory-derivation .

class Premises(h, inc_h)

h: Union[punctilious.core.Formula, punctilious.core.FormulaStatement, punctilious.core.CompoundFormula, tuple, list]: Alias for field number 0

inc_h: Union[punctilious.core.Formula, punctilious.core.FormulaStatement, punctilious.core.CompoundFormula, tuple, list]: Alias for field number 1

construct_formula(h, inc_h)

This python method verify the syntactic correctness of the premises, but does not verify the validity of the premises, it then applies the inference-rule algorithm, and returns a formula.

Note

Note the critical distinction between the construct_formula and the infer_formula_statement methods. The former only verifies the syntactic correctness but does not verify the validity of the premises, it then applies the inference-rule algorithm, and produces a formula that may be invalid . The later verifies the validity of the premises, applies the inference-rule algorithm, and produces a formula-statement that is valid by definition.

Taking the modus-ponens inference-rule as an example, the construct_formula method requires two premise arguments: p_implies_q and p. One may pass a formula as the p_implies_q argument that is not valid in the theory-derivation under consideration, but that is syntactically correct. On the other hand, the infer_formula_statement method requires that both premise arguments be valid.

This distinction makes it possible to use the algorithms of inference-rules in “what if” scenarii, i.e. building invalid formulae. And at the same time, it assures that all formula_statements are valid.

Return type: CompoundFormula