An extended relational algebra with universally or existentially quantified classes as attribute values is discussed. The author builds on his work from the late 1980s [1], in which he introduced the INCINERATE data model. (The acronym is drawn from the phrase, “incorporating inheritance in a relational database.”)

Section 2 introduces the logical foundations of the model. In principle, this model covers hierarchical relations allowing sets of values to be attribute values. To formalize the model, the author uses a modification of standard default logic, in which a relation is conceived as a set of assertions considered as logical formulas in prenex normal form. Informally, an INCINERATE database comprises one or more class hierarchies and a set of relations whose attribute values are chosen from these classes. Quantification over classes is permitted. Thus, partial information is handled through the use of the existential quantifier over arbitrary classes. An exception-refinement mechanism for inheritance is also used. A single logical inference rule is presented that is sufficient to provide a sound and, within limits, complete theorem-proving mechanism for all the assertions in a given relation. Structurally, if the hierarchical relation is flattened, we obtain Codd’s maybe relations.

Section 3 describes the extended relational algebra. Each relation in this algebra constitutes a seminormal ordered default theory. This fact makes it possible to define the relational algebra over hierarchical relations via extensions having the form of flat relations. The goal of section 4 is to develop an implementation of the defined data model as a layer on top of a recent relational DBMS.

Finally, the paper describes the expressive power of the proposed model. It is less than full first-order logic, but the model gives a more expressive treatment of incomplete information. The drawback of this section is that any connection to recent research papers on the expressivity of nested relations is missing.

Unfortunately, the paper is hard to read. Its informal parts dominate the formal ones. Minor mistakes occur in the text. Nevertheless, the theory is interesting, and implementation issues seem to be worth considering. In particular, the approach could be beneficial for knowledge-based information systems.