Some rules are controversial, especially rule three, because of the debate on three-valued logic.

The presence of null values leads to three-valued logic.

Reichenbach also suggested applying a three-valued logic to quantum mechanics.

Strictly, this is a three-valued logic with two-valued functions.

(Despite the title, this is almost entirely about three-valued logics.)

For example, the three-valued logic Ł3 of Łukasiewicz can be axiomatized as:

For an elementary introduction to the three-valued instantiation Ł, see three-valued logic.

The simplest Kleene algebra of this kind is Kleene's three-valued logic K3.

While Łukasiewicz seems to have spent more time on three-valued logic than any other system, he said that one could keep increasing the number of truth values indefinitely.

The three-valued logic that the weapon's operating system ran on was characteristic of Conjoiner programming, but it was also devilishly hard to debug.

He invented a popular shape analysis based on three-valued logic together with Mooly Sagiv and Tom Reps.

Small entoptics surrounded his seated figure, symbols of Boolean and three-valued logics and long cascades of binary.

Motoike I., Adamatzky A. "Three-valued logic gates in reaction-diffusion excitable media."

Contradicting the principle of bivalence, Buridan implies a system of three-valued logic in which there are three truth values--true, false, and some indeterminate third value.

However, because of this simplicity, the intended semantics of Reichenbach's three-valued logic is unsuited to provide a foundation for quantum mechanics that can account for observables.

Codd's theorem also doesn't consider SQL nulls and the three-valued logic they entail; the logical treatment of nulls remains mired in controversy.

For example, in a three-valued logic, sometimes the two greatest truth-values (when they are represented as e.g. positive integers) are designated and the rules of inference preserve these values.

SQL's NULL construct was intended to be part of a three-valued logic system, but fell short of that due to logical errors in the standard and in its implementations.

Examples of logics which have involutive negation are Kleene and Bochvar three-valued logics, Łukasiewicz many-valued logic, fuzzy logic IMTL, etc.

For example, the three-valued Logic of Paradox (LP) validates the law of excluded middle, but not the law of non-contradiction, (P P), and its intended semantics is not bivalent.

Claude Rubinson, Nulls, Three-Valued Logic, and Ambiguity in SQL: Critiquing Date's Critique, SIGMOD Record, December 2007 (Vol.

Thus, he wrote: "if 0 is interpreted as falsehood, 1 as truth, and other numbers in the interval 0-1 as the degrees of probability corresponding to various possibilities, a many-valued logic is obtained which is expansion of three-valued logic and differs from the latter in certain details."

The addition of IS UNKNOWN to the other operators of SQL's three-valued logic makes the SQL three-valued logic functionally complete, meaning its logical operators can express (in combination) any conceivable three-valued logical function.