In their logico-semantic theories Frege and Russell distinguished between a proposition, the judgement that it is true, and the assertion of this judgement. Their distinction, however, fell into oblivion in the course of later developments and was replaced by the formalistic notion of an expression derivable by means of purely syntactical rules of inference. Recently, however, Frege and Russell's original distinction has received renewed interest due to the work of logicians and philosophers such as, for example, Michael Dummett, Per Martin-Löf, and Dag Prawitz, who have pointed to the central importance of both the act of assertion and its justification to logic itself as well as to an adequate theory of meaning and understanding. The contributions to the present volume deal with central issues raised by these authors and their canonical predecessors: What kind of propositions are there and how do they relate to truth? How are propositions grasped by human subjects? And how do these subjects judge those propositions according to various dimensions (such as that of truth and falsehood)? How are those judgements encoded into natural language, communicated to other subjects, and decoded by them? What does it mean to proceed by inference from premiss assertions to a new judgement? The volume contains articles by: S. Bab, H. M. Gärtner, S. Kelter, M. Kracht, B. Mahr, J. Michaelis, D. Prawitz, K. Robering, and T. Wieczorek.