Principal disjunctive paradigm is the content of a course called discrete mathematics in college mathematics. In the mathematical logic part of discrete mathematics, some propositions can be simplified or deduced by truth table and equivalent algorithm, but when the number of independent variables of a proposition is large, the above method is inconvenient, so it is necessary to formulate the proposition into principal conjunctive normal form and principal disjunctive paradigm.

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.