This open access book makes a case for extending logic beyond its traditional boundaries, to encompass not only statements but also also questions. The motivations for this extension are examined in ...detail. It is shown that important notions, including logical answerhood and dependency, emerge as facets of the fundamental notion of entailment once logic is extended to questions, and can therefore be treated with the logician’s toolkit, including model-theoretic constructions and proof systems. After motivating the enterprise, the book describes how classical propositional and predicate logic can be made inquisitive—i.e., extended conservatively with questions—and what the resulting logics look like in terms of meta-theoretic properties and proof systems. Finally, the book discusses the tight connections between inquisitive logic and dependence logic.
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the ...properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His ...philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.
This textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories. The book also ...presents a logical approach to engineering correct software.
Dynamic Epistemic Logic van Ditmarsch, Hans; van der Hoek, Wiebe; Kooi, Barteld
2007, 2007-05-30, Letnik:
337
eBook
Odprti dostop
Dynamic Epistemic Logic is the logic of knowledge change. This is not about one logical system, but about a whole family of logics that allows us to specify static and dynamic aspects of multi-agent ...systems. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also contains exercises including answers and is eminently suitable for graduate courses in logic. A sweeping chapter-wise outline of the content of this book is the following. The chapter 'Introduction' informs the reader about the history of the subject, and its relation to other disciplines. 'Epistemic Logic' is an overview of multi-agent epistemic logic - the logic of knowledge - including modal operators for groups, such as general and common knowledge. 'Belief Revision' is an overview on how to model belief revision, both in the 'traditional' way and in a dynamic epistemic setting. 'Public Announcements' is a detailed and comprehensive introduction to the logic of knowledge to which dynamic operators for truthful public announcement are added. Many interesting applications are also presented in this chapter: a form of cryptography for ideal agents also known as 'the Russian cards problem', the sum-and-product riddle, etc. 'Epistemic Actions' introduces a generalization of public announcement logic to more complex epistemic actions. A different perspective on that matter is independently presented in 'Action Models'. 'Completeness' gives details on the completeness proof for the logics introduced in 'Epistemic Logic', 'Public Announcements', and 'Action Models'. 'Expressivity' discusses various results on the expressive power of the logics presented.
This comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory updates the author's work over the past 12 years, and describes the latest general ideas and open ...problems in this expanding field.
