lancejpollard / cnf.js

Convert Proposition Trees to Conjunctive Normal Form (CNF) or Disjunctive Normal Form (DNF)

CNF.js

NOT WORKING, WORK IN PROGRESS.

Convert propositional formula trees into Conjunctive Normal Form (CNF). Might also convert predicate formulae to CNF as well.

const CNF = require('@lancejpollard/cnf.js')

CNF.convert()

Data Structure

There are 2 main types, which are all subtypes of formula: variable, and connective. There are 3 types of connective: negation, disjunction and conjunction.

Variable

Such as X.

{
  type: 'variable',
  name: string,
  value: boolean,
}

Negation

Such as ¬X.

{
  type: 'negation',
  formula: formula
}

Disjunction

Such as (A ∨ B).

{
  type: 'disjunction',
  base: formula,
  head: formula,
}

Conjunction

Such as (A ∧ B).

{
  type: 'conjunction',
  base: formula,
  head: formula,
}

Equivalencies

Every propositional formula can be converted into an equivalent formula that is in CNF. This transformation is based on rules about logical equivalences: double negation elimination, De Morgan's laws, and the distributive law.

Equivalency	Name
p∧⊤≡p p∨⊥≡p	Identity laws
p∨⊤≡⊤ p∧⊥≡⊥	Domination laws
p∨p≡p p∧p≡p	Idempotent or tautology laws
¬(¬p)≡p	Double negation law
p∨q≡q∨p p∧q≡q∧p	Commutative laws
(p∨q)∨r≡p∨(q∨r) (p∧q)∧r≡p∧(q∧r)	Associative laws
p∨(q∧r)≡(p∨q)∧(p∨r) p∧(q∨r)≡(p∧q)∨(p∧r)	Distributive laws
¬(p∧q)≡¬p∨¬q ¬(p∨q)≡¬p∧¬q	De Morgan's laws
p∨(p∧q)≡p p∧(p∨q)≡p	Absorption laws
p∨¬p≡⊤ p∧¬p≡⊥	Negation laws

HT

• How to convert a propositional formula to conjunctive normal form (CNF)?
• How to convert to conjunctive normal form?