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propositional logic, Boolean algebra, Heyting algebra: is false when A is true and B is false but true otherwise. may mean the same as (the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols).
When drawing a logic symbol, one passes through each square with assigned F values while stopping in a square with assigned T values. In the extreme examples, the symbol for tautology is a X (stops in all four squares), while the symbol for contradiction is an O (passing through all squares without stopping). The square matrix corresponding to ...
In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false.A Boolean expression may be composed of a combination of the Boolean constants True/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.
The Boolean data type is primarily associated with conditional statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean condition evaluates to true or false. It is a special case of a more general logical data type—logic does not always need to be Boolean (see probabilistic logic).
The equality predicate (usually written '=') is also treated as a logical constant in many systems of logic. One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; [1] that is, what special feature of certain constants makes them logical in nature? [2] Some symbols that are commonly treated as logical ...
Logical constants are always given the same meaning by every interpretation of the standard kind, so that only the meanings of the non-logical symbols are changed. Logical constants include quantifier symbols ∀ ("all") and ∃ ("some"), symbols for logical connectives ∧ ("and"), ∨ ("or"), ¬ ("not"), parentheses and other grouping symbols ...
Since predicates are non-logical symbols, they can denote different relations depending on the interpretation given to them. While first-order logic only includes predicates that apply to individual objects, other logics may allow predicates that apply to collections of objects defined by other predicates.
IMPLY can be denoted in algebraic expressions with the logic symbol right-facing arrow (→). Logically, it is equivalent to material implication, and the logical expression ¬A v B. There are two symbols for IMPLY gates: the traditional symbol and the IEEE symbol. For more information see Logic gate symbols.