What is normal form in discrete mathematics?

A formula which is equivalent to a given formula and which consists of a sum of elementary products is called a disjunctive normal form of given formula. Example : (P ∧ ~ Q) ∨ (Q ∧ R) ∨ (~ P ∧ Q ∧~ R) The DNF of formula is not unique.

What is normal form formula in logic?

In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.

What is normal forms in artificial intelligence?

Conjunctive normal form (CNF) is an approach to Boolean logic that expresses formulas as conjunctions of clauses with an AND or OR. Each clause connected by a conjunction, or AND, must be either a literal or contain a disjunction, or OR operator. CNF is useful for automated theorem proving.

What is normal logic form?

In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept.

What are CNF formulas?

A CNF formula is a restricted special case. It is a conjunction of “clauses,” each of which is a disjunction of “literals,” each of which is either a variable or a negated variable.

What is PCNF and PDNF?

Every PDNF or PCNF corresponds to a unique Boolean Expression and vice versa. If X and Y are two Boolean expressions then, X is equivalent to Y if and only if PDNF(X) = PDNF(Y) or PCNF(X) = PCNF(Y).

What is disjunctive normal form of P ∧ P -> Q?

The normal form for this is p ∧ ~q, but since this matches a false output, it will need to be negated. Hence the normal form here is actually ~(p ∧ ~q). Since there are no other normal forms, this will also be considered the disjunctive normal form.

What is clause normal form?

Clause Normal Form (CNF) is a sub-language of 1st order logic. A clause is an expression of the form L1 |… | Lm where each Li is a literal. An empty cause has no literals, and no models. Clauses are denoted by uppercase letters with a superscript |, e.g., C|.