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This book argues that in order to account for the compositional behavior of many near-synonymous items, semantic analyses need to pay close attention to at least two semantic dimensions: standard assertions and conventional implicatures, which express additional side comments. The discussed phenomena are clausal adjuncts and complements in German. The new analysis of 'weil' and 'denn' ('because') shows that both contribute the same semantic operator, but one as an assertion, the other as a conventional implicature. This explains why only 'denn' can have speech-act modifying uses. This novel two-dimensional analysis is extended to other sentence adjuncts such as regular vs. relevance conditionals, although-clauses, and sentence adverbs. Further, the book investigates certain complement clauses. It analyzes sliftings as evidential-like parentheticals which contribute their meaning on the conventional implicature dimension. In contrast, German embedded verb-second clauses are shown to be truly embedded and analyzed as operating in the assertion dimension. The verb-second syntax is shown to contribute an additional epistemic component on the conventional implicature dimension.