1. Introduction 2. A generative grammar as an algorithm 3. The semantic component 4. Bibliography 1. Introduction Throughout the 20th century up to the present day grammar and semantics have been uneasy bedfellows. A look at the historical background will make it clear how this curious situation came about. 20th-century linguistics has been characterized by an almost exclusive concern with the structure of words, word groups and sentences. This concern was reinforced, especially on the American side of the Atlantic, by the sudden rise and subsequent dominance of behaviorism during the 1920s. It started in psychology but quickly permeated all the human sciences, including linguistics, until the early 1960s, when it collapsed as suddenly as it had arisen.