Abstract Propositional modal logics can be extended by propositional quantifiers, i.e. quantifiers binding proposition letters understood as variables. This paper investigates whether such an extension is always conservative. It is shown that the answer depends on the way in which propositional quantifiers are added. On a minimal approach, according to which propositional quantifiers only have to satisfy the classical principles of quantification, every classical modal logic has a conservative extension by propositional quantifiers. However, in the context of normal modal logics it is natural to require propositionally quantified extensions also to be closed under the rule of necessitation. It is shown that in this setting, there are normal modal logics whose propositionally quantified extensions are nonconservative. Nonconservativity is shown to be a special case of a number of model-theoretic notions of incompleteness. More tentatively, it is suggested that nonconservativity indicates incompleteness in a more substantial sense, concerning the intended target of capturing the logics of modalities.

Abstract Propositional modal logic over relational frames is naturally extended with propositional quantifiers by letting them range over arbitrary sets of worlds of the relevant frame. This is also known as second-order propositional modal logic. The propositionally quantified modal logic of a class of relational frames is often not axiomatizable, although there are known exceptions, most notably the case of frames validating the strong modal logic $\mathrm {S5}$ . Here, we develop new general methods with which many of the open questions in this area can be answered. We illustrate the usefulness of these methods by applying them to a range of examples, which provide a detailed picture of which normal modal logics define classes of relational frames whose propositionally quantified modal logic is axiomatizable. We also apply these methods to establish new results in the multimodal case.

This paper describes the development of the RWTH Mandarin LVCSR system. Different acoustic front-ends together with multiple system cross-adaptation are used in a two stage decoding framework. We describe the system in detail and present systematic recognition results. Especially, we compare a variety of approaches for cross-adapting to multiple systems. During the development we did a comparative study on different methods for integrating tone and phoneme posterior features. Furthermore, we apply lattice based consensus decoding and system combination methods. In these methods, the effect of minimizing character instead of word errors is compared. The final system obtains a character error rate of 17.7% on the GALE 2006 evaluation data.