logicalconstraint

A logical constraint is a condition or relation that must hold among variables in a system, expressed in a logical formalism. It restricts the set of permissible assignments and thereby defines the feasible solutions of a problem. Logical constraints can be stated in various logics, including propositional logic, first-order logic, or specialized constraint languages used in constraint programming.

In constraint satisfaction problems, logical constraints specify allowable combinations of values for variables. A solution is an assignment that satisfies all constraints. Common binary constraints include inequality (x ≠ y) or order relations (x < y). Constraints can be extended to arity greater than two and may involve quantifiers in first-order form.

Solving techniques include encoding the constraints as SAT problems with boolean variables and clauses, or using a constraint solver that propagates domains (arc consistency) and performs search. Constraint programming languages such as MiniZinc allow high-level specification of logical constraints and automatically select suitable solving methods.

Applications of logical constraints span scheduling, resource allocation, verification, and knowledge representation. The computational complexity depends on the logical formalism and the structure of the constraints; in general, satisfiability of arbitrary conjunctions of constraints is NP-complete, though decidable theories and restricted constraint families can yield tractable solving.