BelnapDunnLogik

Belnap-Dunn Logic, often written Belnap–Dunn logic and abbreviated BD, is a four-valued logical system developed by Nuel Belnap and Joseph Dunn in the 1970s to model reasoning with incomplete and potentially conflicting information. It is both paraconsistent and paracomplete: it allows contradictions without explosive entailment and accommodates truth-value gaps.

The language uses four truth values: true (t), false (f), both true and false (b), and neither true nor false (n). The semantics are typically given in a bilattice framework, which combines a truth order and a knowledge (information) order. In the truth order, t represents a stronger form of truth than f; in the knowledge order, n contains no information and b contains both information about truth and falsity. Operators are defined by truth tables extended from classical connectives. Negation swaps t and f, while b and n are fixed under negation (neg(b) = b, neg(n) = n). Conjunction and disjunction, as well as implication, are defined to respect both orders, yielding behavior that coincides with classical logic on the values t and f but behaves differently when b or n are involved.

BD is studied as a prototype of paraconsistent logics and as an example of bilattice-based semantics. It has influenced later formalisms for inconsistent or incomplete information, and it is often contrasted with three-valued logics such as Kleene’s and with other four-valued systems. Applications include databases, knowledge representation, and static analysis where information may be incomplete or contradictory.