From the point of view of distributed programming one of the most interesting communication mechanisms is associative tuple matching in a shared dataspace, as exemplified in the Linda coordination language. Linda has been used as a coordination layer to parallelize several sequential programming languages, such as C and Scheme. In this paper we study the combination of Linda with a logic language, whose result is the language Extended Shared Prolog (ESP). We show that ESP is based on a new programming model called PoliS, that extends Linda with Multiple Tuple Spaces. A class of applications for ESP is discussed, introducing the concept of ``open multiple tuple spaces''. Finally, we show how the distributed implementation of ESP uses the network version of Linda's tuple space.