conditionsrelations

Conditionsrelations is a term used in theoretical computer science and logic to describe the study of how logical conditions (predicates or constraints) relate to relational structures (such as graphs, databases, or sets of ordered tuples). The idea is to formalize how a collection of conditions interacts with relations that connect elements of a domain, and how these interactions shape what counts as a valid configuration or solution.

Formal framework: let D be a domain. A condition is a predicate on D or on tuples from D. A relation is a subset of D^k for some k. A conditionsrelation consists of a set C of conditions and a set R of relations together with a specification that binds each condition to particular relations or variables. A model M, or assignment of values to variables, satisfies the conditions relative to the relations if all predicates hold in M and the tuples in the relations meet the same constraints. The framework supports operations such as conjunction of conditions, existential and universal quantification, and relational joins to form compound constraints.

Examples illustrate the idea: in a simple user database, conditions might include IsAdult(x) and HasEmail(x); the relation is Friend(x,y) or WorksWith(x,y). A conditionsrelation could express that every adult user has at least one email and, if two users are friends, certain conditions hold for their attributes. In constraint satisfaction problems, conditions define predicates on variables and relations enforce how variables can be jointly assigned.

Relation to related concepts: it overlaps with constraint satisfaction problems, first-order logic, and relational algebra and database constraints. It is not a standard, widely adopted term, but is used in some discussions to organize how conditions and relations constrain a system.

See also: constraint satisfaction problem, first-order logic, relational database, relational algebra, rule-based systems.