A new bidirectional optical associative processor is described for searching a hierarchical database that is stored as an adjacency matrix. The paper discusses how the processor can answer relatively complex queries on a knowledge base when the queries are formulated as combinations of set closures, unions, intersections, and complementations. Thus, a processor that performs general set operations results, as well as a system that can answer various knowledge base queries and guide a knowledge base search. These are new operations for associative processors that increase their utility. This new associative processor operates on entities and their attributes. It can be viewed as a type lattice processor (since the entities and attributes form a hierarchy known as a type lattice), as a closure processor (since it performs closure operations that list all attributes of an entity [or entities] or all entities with a given attribute [or attributes]), or as an adjacency processor (since the connection matrix used stores adjacent associations of attributes and entities).