Properties and Modeling of Partial Conjunction / Disjunction

The partial conjunction/disjunction function (PCD) integrates conjunctive and disjunctive features in a single function. Special cases of this function include the pure conjunction, the pure disjunction, and the arithmetic mean. PCD enables a continuous transition from the pure conjunction to the pure disjunction, using a parameter that specifies a desired level of conjunction (andness) or disjunction (orness). In this paper, we investigate and compare various approaches to organize the PCD function. Our goal is to specify the most important necessary conditions that the PCD should satisfy. The next step would then be to derive the best version of PCD and use it to create other compound continuous logic functions. Key-Words: Continuous logic, preferences, andness, orness, partial conjunction/disjunction, andor, orand