https://github.com/lancejpollard/cnf.js

Convert Proposition Trees to Conjunctive Normal Form (CNF) or Disjunctive Normal Form (DNF)
https://github.com/lancejpollard/cnf.js

conjunctive-normal-form math proof-theory propositional-logic

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

• Host: GitHub
• URL: https://github.com/lancejpollard/cnf.js
• Owner: lancejpollard
• Created: 2022-01-24T06:03:55.000Z (almost 3 years ago)
• Default Branch: make
• Last Pushed: 2022-01-25T03:13:49.000Z (almost 3 years ago)
• Last Synced: 2024-09-10T09:16:51.056Z (4 months ago)
• Topics: conjunctive-normal-form, math, proof-theory, propositional-logic
• Language: JavaScript
• Homepage:
• Size: 3.91 KB
• Stars: 0
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: readme.md

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README

        

# CNF.js

NOT WORKING, WORK IN PROGRESS.

Convert propositional formula trees into [Conjunctive Normal Form](https://en.wikipedia.org/wiki/Conjunctive_normal_form) (CNF). Might also convert [predicate formulae](https://en.wikipedia.org/wiki/First-order_logic) to CNF as well.

```js

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.

```js

{

  type: 'variable',

  name: string,

  value: boolean,

}

```

### Negation

Such as ¬X.

```js

{

  type: 'negation',

  formula: formula

}

```

### Disjunction

Such as (A ∨ B).

```js

{

  type: 'disjunction',

  base: formula,

  head: formula,

}

```

### Conjunction

Such as (A ∧ B).

```js

{

  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](https://en.wikipedia.org/wiki/Logical_equivalence): 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)?](https://stackoverflow.com/a/9533548/169992)

- [How to convert to conjunctive normal form?](https://math.stackexchange.com/questions/214338/how-to-convert-to-conjunctive-normal-form)