Generalized conjunction/disjunction

The generalized conjunction/disjunction function (GCD) is a continuous logic function of two or more variables that integrates conjunctive and disjunctive properties in a single function. It is used as a mathematical model of simultaneity and replaceability of inputs. Special cases of this function include the full (pure) conjunction, the partial conjunction, the arithmetic mean, the partial disjunction, and the full (pure) disjunction. GCD enables a continuous transition from the full conjunction to the full disjunction, using a parameter that specifies a desired level of conjunction (andness) or disjunction (orness). In this paper, we investigate and compare various versions of GCD and other mathematical models of simultaneity and replaceability that are applicable in the areas of system evaluation, and information retrieval.