One of the distinguishing characteristics of a data stream system is ?a continuous query operating on dynamic data? as opposed to ?static data processed by instantaneous query? in DBMS. Due to potentially infinite size of the stream a query is evaluated after forming finite subsets of the data stream. The sliding window model is the most suitable model for processing finite subsets of a data stream where only recent data items qualify.

In this paper, we propose a mathematical model to express a continuous query on sliding windows. This model expresses a window as an ordered set. Its sliding mechanism is expressed through a set of transition operations and query evaluation is expressed through a set of output operations.