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