precedences

Precedence is the notion of priority or order assigned to elements within a system, guiding how decisions, actions, or evaluations proceed. The term is used across disciplines—from formal logic and computer science to social protocol and historical analysis—where it helps resolve competing factors and reduce ambiguity.

In mathematics and computing, operator precedence determines how expressions are parsed. Multiplication and division typically bind more tightly than addition and subtraction, and parentheses override default rules. In many programming languages, precedence together with associativity defines how expressions are evaluated from left to right. For example, 2 + 3 * 4 evaluates to 14, not 20.

Temporal precedence concerns the ordering of events in time and causality. An event is said to have precedence over another if it occurs earlier or serves as a cause. In historiography and logic, establishing precedence clarifies sequences and dependencies.

Ceremonial and legal precedence, also called protocol precedence, governs rank and placement in formal settings. It affects seating arrangements, right of way, and delegation of authority in ceremonies, courts, and government operations. Such precedence reflects social, institutional, or legal hierarchies and expectations.

In mathematics, a precedence relation is a binary relation that expresses priority. Often it is a partial or total order and is used in ordering, scheduling, and constraint systems. Precedence notions also appear as constraints in project planning and as rules in compiler design.