In this paper, we propose an extended relational model, named Pv-table, for representing exclusive disjunctive data (i.e., there exists a set of possible values for a data item, and exactly one of the possible values is true) by associating partial values and variables with attributes. While a partial value denotes the set of possible values, a variable serves as an identifier for the true value of the data item. Identifiers can be used to determine the equi-relationship among partial values. The relational operators are extended to manipulate Pv-tables. We show that the set-based query evaluation on Pv-tables is sound and complete for queries consisting of extended selection, union, intersection, Cartesian product and join. We also show that useful algebraic properties are preserved in our model. A disjunctive (resp. conjunctive) query can be replaced by the extended union (resp. intersection) of the two corresponding subqueries. These properties provide a more natural interpretation of queries. They also facilitate query decomposition process for optimizing distributed queries. These properties are not preserved for many other extended models.