Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.

This paper investigates a generalized version of inquisitive semantics. A complete axiomatization of the associated logic is established, the connection with intuitionistic logic and several intermediate logics is explored, and the generalized version of inquisitive semantics is argued to have certain advantages over the system that was originally proposed by Groenendijk (2009) and Mascarenhas (2009).

In Context and Content Robert Stalnaker develops a philosophical picture of the nature of speech and thought and the relations between them. Two themes in particular run through these collected essays: the role that the context in which speech takes place plays in accounting for the way language is used to express thought, and the role of the external environment in determining the contents of our thoughts. Stalnaker argues against the widespread assumption of the priority of linguistic over mental representation, (...) which he suggests has had a distorting influence on our understanding. The first part of the book develops a framework for representing contexts and the way they interact with the interpretation of what is said in them. This framework is used to help to explain a range of linguistic phenomena concerning presupposition and assertion, conditional statements, the attribution of beliefs, and the use of names, descriptions, and pronouns to refer. Stalnaker then draws out the conception of thought and its content that is implicit in this framework. He defends externalism about thought--the assumption that our thoughts have the contents they have in virtue of the way we are situated in the world--and explores the role of linguistic action and linguistic structure in determining the contents of our thoughts. Context and Content offers philosophers and cognitive scientists a summation of Stalnaker's important and influential work in this area. His new introduction to the volume gives an overview of this work and offers a convenient way in for those who are new to it. The Oxford Cognitive Science series is a new forum for the best contemporary work in this flourishing field, where various disciplines--cognitive psychology, philosophy, linguistics, cognitive neuroscience, and computational theory--join forces in the investigation of thought, awareness, understanding, and associated workings of the mind. Each book constitutes an original contribution to its subject, but will be accessible beyond the ranks of specialists, so as to reach a broad interdisciplinary readership. The series will be carefully shaped and steered with the aim of representing the most important developments in the field and bringing together its constituent disciplines. (shrink)

This paper gives a new, purely semantic proof of the following theorem: if an intermediate propositional logic L has the disjunction property then a disjunction free formula is provable in L iff it is provable in intuitionistic logic. The main idea of the proof is to use the well-known semantic criterion of the disjunction property for "simulating" finite binary trees (which characterize the disjunction free fragment of intuitionistic logic) by general frames.

In classical logic, the proposition expressed by a sentence is construed as a set of possible worlds, capturing the informative content of the sentence. However, sentences in natural language are not only used to provide information, but also to request information. Thus, natural language semantics requires a logical framework whose notion of meaning does not only embody informative content, but also inquisitive content. This paper develops the algebraic foundations for such a framework. We argue that propositions, in order to embody (...) both informative and inquisitive content in a satisfactory way, should be defined as non-empty, downward closed sets of possibilities, where each possibility in turn is a set of possible worlds. We define a natural entailment order over such propositions, capturing when one proposition is at least as informative and inquisitive as another, and we show that this entailment order gives rise to a complete Heyting algebra, with meet, join, and relative pseudo-complement operators. Just as in classical logic, these semantic operators are then associated with the logical constants in a first-order language. We explore the logical properties of the resulting system and discuss its significance for natural language semantics. We show that the system essentially coincides with the simplest and most well-understood existing implementation of inquisitive semantics, and that its treatment of disjunction and existentials also concurs with recent work in alternative semantics. Thus, our algebraic considerations do not lead to a wholly new treatment of the logical constants, but rather provide more solid foundations for some of the existing proposals. (shrink)

In this paper, Carnap's modal logic C is reconstructed. It is shown that the Carnapian approach enables us to create some epistemic logics in a relatively straightforward way. These epistemic modifications of C are axiomatized and one of them is compared with intuitionistic logic. At the end of the paper, some connections between this epistemic logic and Medvedev's logic of finite problems and inquisitive semantics are shortly discussed.