Deixis verges on the borderline of philosophy, semantics and pragmatics. Since no satisfactory theory of deixis has been proposed so far, this book gives a critical examination of the state of the art and suggests a solution within the framework of discourse analysis. The deictic systems of English and Polish are compared in termes of algorithms, which determine the distribution of demonstrative pronouns in the two languages. Many difficulties found in other approaches can be escaped through the application of algorithms accounting for the speaker's choices in his use of demonstratives during the discourse flow.