Since Kripke, philosophers have distinguished a priori true statements from necessarily true ones. A statement is a priori true if its truth can be established before experience, and necessarily true if it could not have been false according to logical or metaphysical laws. This distinction can be captured formally using two-dimensional semantics. There is a natural way to extend the notions of apriority and necessity so they can also apply to questions. Questions either can or cannot be resolved before experience, (...) and either are or are not about necessary facts. Classical two-dimensionalism has no account of question meanings, so it has to be combined with a framework for question semantics in order to capture these observations. It is shown in [14] how two-dimensional semantics can be combined with inquisitive semantics, in which questions are analyzed in terms of information. The present paper investigates the logic of two-dimensional inquisitive semantics, and provides a complete proof system. (shrink)

Information exchange can be viewed as a process of asking questions and answering them. While dynamic epistemic logic traditionally focuses on statements, recent developments have been concerned with ways of incorporating questions. One approach, based on the framework of inquisitive semantics, is inquisitive dynamic epistemic logic ). In this system, agents are represented with issues as well as information. On the dynamic level, it can model actions that raise new issues. Compared to other approaches, a limitation of \ is that (...) it can only encode public announcements. \ can be refined to encode private questions, by merging its static basis, inquisitive epistemic logic ), with action model logic ). This can be done in two ways, namely by enriching action models with questions as possible actions or with issues concerning which action takes place. This paper describes the corresponding dynamic logics, which are conservative extensions of both \ and \, and a sound and complete axiomatization is given for both. (shrink)

The truth conditions of sentences with indexicals like ‘I’ and ‘here’ cannot be given directly, but only relative to a context of utterance. Something similar applies to questions: depending on the semantic framework, they are given truth conditions relative to an actual world, or support conditions instead of truth conditions. Two-dimensional semantics can capture the meaning of indexicals and shed light on notions like apriority, necessity and context-sensitivity. However, its scope is limited to statements, while indexicals also occur in questions. (...) Moreover, notions like apriority, necessity and context-sensitivity can also apply to questions. To capture these facts, the frameworks that have been proposed to account for questions need refinement. Two-dimensionality can be incorporated in question semantics in several ways. This paper argues that the correct way is to introduce support conditions at the level of characters, and develops a two-dimensional variant of both proposition-set approaches and relational approaches to question semantics. (shrink)