If you have either NAND or NOR as a primitive, you can construct the others from it. Comparisons between any SqlTypes return a SqlBoolean value type. IMX, developers would consider using three valued logic intentionally would be considered an abuse of three valued logic. Most software developers will be intimately familiar with what is popularly known as Boolean logic but should actually be called a two-valued Boolean algebra – a Boolean algebra that is defined on the two truth values True and False, and the three operators AND, OR, and NOT. There are 16 possible dyadic operators for two-valued logic (two inputs, each with one of two possible values, mapping to a result with two possible values = 2^(2^2)). Writing SQL typically involves writing queries to explicitly avoid NULL values in Boolean expressions. Articles Related Example SQL - Boolean Documentation / Reference Three-valued_logic A three-valued logic implements a boolean as having three possible values: true, false and some indeterminate third value. In three unnumbered pages from his unpublished notes written before 1910, Peirce developed what amounts to a semantics for three-valued logic. The System.Data.SqlTypes namespace introduces a SqlBoolean type to represent this 3-value logic. Philosophic Foundations of Quantum Mechanics (University of California, 1944). Peirce's Three-Valued Logic. Of course, there are other systems, some of which represent a more radical change in our way of speaking. Generally speaking from a user standpoint, you don't want a Boolean expression to evaluate to NULL. The UNKNOWN value is represented by the null value of the SqlBoolean type. This is at least ten years before Emil Post's dissertation, which is usually cited as the origin of three-valued logic. There are 19,683 possible dyadic operators for three-valued logic (3^(3^2)). In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean,  sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value. This is hardly surprising in view of the fact that it involves an esoteric Polish mathematician and because it behaves differently in the DDL (Data Declaration Language) and the DML (Data Manipulation Language). In this paper, ‘three-valued logic' means the system presented at the beginning. 7. 4.2 Three-valued logic The principle of bivalence and the law of excluded middle Unlike modal logics, which are extensions of classical (propositional and predicate) logic, three-valued logics are its alternatives, as they abandon one of its basic principles – that of bivalence: The whole subject of the Three-Valued (also known as ternary, trivalent or 3VL) Logic of SQL tends to trip people up. NULL and three-valued logic. A few of the more common examples are: in Balanced ternary, each digit has one of 3 values: −1, 0, or +1; these values may also be … Normally, the result of a logical expression is TRUE or FALSE. For example, at the time of recording the customer information, the email may be unknown, so it is recorded as NULL in the database. In the database world, NULL is used to indicate the absence of any data value. 6. As with bivalent logic, truth values in ternary logic may be represented numerically using various representations of the ternary numeral system.
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