Canonical normal formIn Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF) or minterm canonical form, and its dual, the canonical conjunctive normal form (CCNF) or maxterm canonical form. Other canonical forms include the complete sum of prime implicants or Blake canonical form (and its dual), and the algebraic normal form (also called Zhegalkin or Reed–Muller). Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables.
Boolean circuitIn computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length. Boolean circuits are defined in terms of the logic gates they contain. For example, a circuit might contain binary AND and OR gates and unary NOT gates, or be entirely described by binary NAND gates. Each gate corresponds to some Boolean function that takes a fixed number of bits as input and outputs a single bit.
Algebraic logicIn mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected problems like representation and duality. Well known results like the representation theorem for Boolean algebras and Stone duality fall under the umbrella of classical algebraic logic .
Łukasiewicz logicIn mathematics and philosophy, Łukasiewicz logic (ˌluːkəˈʃɛvɪtʃ , wukaˈɕɛvitʂ) is a non-classical, many-valued logic. It was originally defined in the early 20th century by Jan Łukasiewicz as a three-valued modal logic; it was later generalized to n-valued (for all finite n) as well as infinitely-many-valued (א0-valued) variants, both propositional and first order. The א0-valued version was published in 1930 by Łukasiewicz and Alfred Tarski; consequently it is sometimes called the ŁukasiewiczTarski logic.
Boolean-valued modelIn mathematical logic, a Boolean-valued model is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the truth values of propositions are not limited to "true" and "false", but instead take values in some fixed complete Boolean algebra. Boolean-valued models were introduced by Dana Scott, Robert M. Solovay, and Petr Vopěnka in the 1960s in order to help understand Paul Cohen's method of forcing. They are also related to Heyting algebra semantics in intuitionistic logic.
