## Abstract

Based on the semantic concepts developed by M. Dunn and N. Belnap,

a four-valued language containing only two logical symbols is proposed. We

show that this language is functionally complete with regard to the given

semantics. Specifically, we prove that every truth-function is expressed by

a formula of the language. To do this, we define two concepts akin to the

disjunctive and conjunctive normal forms. Using these concepts, we establish

that every truth-function for a four-valued semantics can be represented

by a formula in a disjunctive form or in a conjunctive form.

a four-valued language containing only two logical symbols is proposed. We

show that this language is functionally complete with regard to the given

semantics. Specifically, we prove that every truth-function is expressed by

a formula of the language. To do this, we define two concepts akin to the

disjunctive and conjunctive normal forms. Using these concepts, we establish

that every truth-function for a four-valued semantics can be represented

by a formula in a disjunctive form or in a conjunctive form.

Original language | English |
---|---|

Pages (from-to) | 579 - 588 |

Number of pages | 9 |

Journal | Bulletin of the Belgian Mathematical Society Simon Stevin |

Volume | 22 |

Issue number | 4 |

Publication status | Published - 2015 |

## Keywords

- Four-valued logic
- Functional completeness
- Disjunctive normal form
- Conjunctive normal form