Disjunctive paradigm is the standardization (or normalization) of logical formulas and the disjunction of conjunctive clauses. As a standard form, it is useful in automatic theorem proving. A logical formula is considered as DNF if and only if it is the disjunction of one or more conjunctions of one or more words.
Theorem and proof
1, Theorem: The principal disjunctive paradigm of any nonpermanent hypothesis with n propositional arguments is unique.
2. Prove: Prove by reducing to absurdity.
Suppose the non-permanent hypothesis A(P 1, P2, P3, ... Pn) has two different principal disjunctive paradigms A 1 and A2, then A.
Because A 1 and A2 are two different principal disjunctive paradigms. So at least one minimum term mi only exists in A 1 or A2. We set mi at A 1 instead of A2.
Let mi have a true assignment R in A 1, then the principal disjunctive normal form A 1 is true under assignment R, but the principal disjunctive normal form A2 is false under assignment R, which is different from A 1.
The above contents refer to Baidu Encyclopedia-principal disjunctive paradigm.