Definition:Multi-Value Logic
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Definition
Multi-value logic is a branch of logic in which it is admissible for a statements to have a truth value other than just true or false.
Examples
Arbitrary Example
The following is an approach to multi-value logic which assigns values to statement variables according to the rules:
| \(\ds \size {\lnot A}\) | \(=\) | \(\ds 1 - \size A\) | Definition of Logical Not | |||||||||||
| \(\ds \size {A \lor B}\) | \(=\) | \(\ds \max \set {\size A, \size B}\) | Definition of Disjunction | |||||||||||
| \(\ds \size {A \land B}\) | \(=\) | \(\ds \min \set {\size A, \size B}\) | Definition of Conjunction | |||||||||||
| \(\ds \size {A \implies B}\) | \(=\) | \(\ds \begin {cases} 1 & : \size A \le \size B \\ 1 - \size A + \size B & : \size A < \size B \end {cases}\) | Definition of Implication |
for statement variables $A$ and $B$.
Also known as
Multi-value logic is also known as many-valued logic.
Also see
- Probability theory: an extension of multi-value logic over which truth values are allowed to range over the continuum from true to false.
- Results about multi-value logic can be found here.
Historical Note
The concept of multi-value logic was introduced by Emil Leon Post in $1921$.
Sources
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $1$: Introduction: $\S 1.4$: Non-standard logics
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): many-valued logic
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): many-valued logic