josclauses

Josclauses are a formal construct used in constraint programming and logic to express exclusive disjunction constraints where exactly one literal among a set should be true. The term jos stands for “just one satisfaction” and signals this unique-truth requirement.

Semantics and syntax: A josclause consists of a finite set of literals, where a literal is a variable or its negation. The clause is satisfied in a given assignment if exactly one of the literals evaluates to true. Example: For variables x, y, z, the josclause {x, not y, z} is satisfied when exactly one of x, not y, z is true. In practice, josclauses are used as constraints within larger problems; multiple josclauses combine to form a constraint network.

Relation to other concepts: Josclauses resemble exactly-one constraints and are related to XOR-SAT and cardinality constraints. They can be encoded into standard CNF for SAT solvers using established encodings (pairwise, sequential/ladder). They are used in scheduling, resource allocation, and configuration problems where mutual exclusivity among several options is required.

History and notes: The concept emerged in discussions of enhanced constraint propagation in logic programming and constraint solving. While not as widely standardized as CNF or XOR constraints, josclauses have a niche in problem formulations that require explicit exactly-one semantics. Researchers compare their propagation complexity to other exact-one encodings, guiding solver design and optimization.