The development of any comprehensive proposal for spatio-temporal databases involves significant extensions to many aspects of a non-spatio-temporal architecture. One aspect that has received less attention than most is the development of a query calculus that can be used to provide a semantics for spatio-temporal queries and underpin an effective query optimization and evaluation framework. In this paper, we show how a query calculus for spatio-temporal object databases that builds upon the monoid calculus proposed by Fegaras and Maier for ODMG-compliant database systems can be developed. The paper shows how an extension of the ODMG type system with spatial and temporal types can be accommodated into the monoid approach. It uses several queries over historical (possibly spatial) data to illustrate how, by mapping them into monoid comprehensions, the way is open for the application of a logical optimizer based on the normalization algorithm proposed by Fegaras and Maier.