Abstract. This paper describes a query algebra for tolog, a query language for Topic Maps inspired by Prolog and very similar to Datalog. The language is based on binding variables by matching predicates against the topic map being queried, and contains predicates for querying any aspect of the Topic Maps Data Model (TMDM) [ISO13250-2], as well as support for user-defined predicates. SQL-like features like aggregate functions, projection, ordering, and result set paging are also supported. The paper uses a formal model for Topic Maps called Q to formally define the semantics of tolog. The standard tolog predicates are defined, together with a query algebra. This gives the query language a firm basis, enables interoperable implementations, and serves as the starting point for further work on the language.