relativeor

Relativeor is a term used in theoretical discussions to denote a context-sensitive disjunction operator. Unlike standard logical OR, a relativeor's truth value depends on a reference context or a relation between evaluation contexts.

In a formal setting, a binary relativeor ⊕_R combines propositions P and Q with a context relation R. Under a base context C, P ⊕_R Q is true if Eval(C, P) is true, or if Eval(C', Q) is true for a context C' related to C by R. Variants vary in evaluation order and symmetry, with some definitions allowing P and Q to be evaluated in different or related contexts and others enforcing a specific evaluation sequence.

Interpretation and uses: The concept appears in discussions of context-dependence in linguistics and formal semantics, where the truth of alternatives depends on surrounding assumptions. In theoretical computer science and dynamic logic, a relativeor can model choices that depend on user state, environment, or time. It provides a framework for modeling disjunctions whose meaningfulness shifts as context changes.

Example: Consider P = "Feature A is enabled" and Q = "Feature B is enabled." In context C for an advanced user, Eval(C, P) may be true; in a restricted context C' for a standard user, Eval(C', Q) may be true. The relativeor yields true if either condition holds in its respective context.

See also: disjunction, context sensitivity, dynamic logic, modal logic.