Many database application areas require an ability to handle incomplete and/or inconsistent information. Such information, called paraconsistent information, has been the focus of some recent research. In this paper we present a technique for representing and manipulating paraconsistent information in object-oriented databases. Our technique is based on two new data types for such information. These data types are generalizations of the boolean and bag data types of the Object Data Management Group standard (ODMG). Algebraic operators with a 4- valued paraconsistent semantics are introduced for the new data types. Also a 4-valued operational semantics is presented for the select expression, with an example illustration of how such a semantics can be used effectively to query an object-oriented database containing paraconsistent information. To our knowledge, our technique is the first treatment of inconsistent information in object-oriented databases.