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In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such ...
The propositional calculus[ a ] is a branch of logic. [ 1 ] It is also called propositional logic, [ 2 ]statement logic, [ 1 ]sentential calculus, [ 3 ]sentential logic, [ 1 ] or sometimes zeroth-order logic. [ 4 ][ 5 ] It deals with propositions [ 1 ] (which can be true or false) [ 6 ] and relations between propositions, [ 7 ] including the ...
v. t. e. A truth table is a mathematical table used in logic —specifically in connection with Boolean algebra, Boolean functions, and propositional calculus —which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
Three-valued logic. In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, [1] sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false, and some third value. This is contrasted with the more commonly known bivalent logics (such as classical ...
propositional logic, Boolean algebra, first-order logic. ⊥ {\displaystyle \bot } denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. The proposition. ⊥ ∧ P {\displaystyle \bot \wedge P} is always false since at least one of the two is unconditionally false. ∀.
In classical logic, with its intended semantics, the truth values are true (denoted by 1 or the verum ⊤), and untrue or false (denoted by 0 or the falsum ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of logical connectives are truth functions, whose ...
Existential generalization / instantiation. In propositional logic and Boolean algebra, De Morgan's laws, [1][2][3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician.
SAT solver. In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem. On input a formula over Boolean variables, such as " (x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the ...
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