Advances in Proof-Theoretic Semantics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Proof-Theoretic Semantics write by Thomas Piecha. This book was released on 2015-10-24. Advances in Proof-Theoretic Semantics available in PDF, EPUB and Kindle. This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.
Proof-theoretic Semantics
Proof-theoretic Semantics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof-theoretic Semantics write by Nissim Francez. This book was released on 2015-10-29. Proof-theoretic Semantics available in PDF, EPUB and Kindle. This book is a monograph on the topic of Proof-Theoretic Semantics, a theory of meaning constituting an alternative to the more traditional Model-Theoretic Semantics. The latter regards meaning as truth-conditions (in arbitrary models), the former regards meaning as canonical derivability conditions in a meaning-conferring natural-deduction proof-system. In the first part of the book, the Proof-Theoretic Semantics for logic is presented. It surveys the way a natural-deduction system can serve as meaning-conferring, and in particular analyses various criteria such a system has to meet in order to qualify as meaning-conferring. A central criterion is harmony, a balance between introduction-rules and elimination-rules. The theory is applied to various logics, e.g., relevance logic, and various proof systems such as multi-conclusion natural-deduction and bilateralism. The presentation is inspired by recent work by the author, and also surveys recent developments. In part two, the theory is applied to fragments of natural language, both extensional and intensional, a development based on the author's recent work. For example, conservativity of determiners, once set up in a proof-theoretic framework, becomes a provable property of all (regular) determiners. It is shown that meaning need not carry the heavy ontological load characteristic of Model-Theoretic Semantics of complex natural language constructs. Nissim Francez is an emeritus professor of computer science at the Technion, Israel Institute of Technology. At a certain point in his career he moved from research related to concurrent and distributed programming and program verification to research in computational linguistics, mainly formal semantics of natural language. In recent years, he has worked on Proof-Theoretic Semantics, in particular for natural language.
The Semantics and Proof Theory of the Logic of Bunched Implications
The Semantics and Proof Theory of the Logic of Bunched Implications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Semantics and Proof Theory of the Logic of Bunched Implications write by David J. Pym. This book was released on 2013-04-17. The Semantics and Proof Theory of the Logic of Bunched Implications available in PDF, EPUB and Kindle. This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.
What Logics Mean
What Logics Mean - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook What Logics Mean write by James W. Garson. This book was released on 2013-11-14. What Logics Mean available in PDF, EPUB and Kindle. This book explains how the meanings of the symbols of logic are determined by the rules that govern them.
Proof and Falsity
Proof and Falsity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof and Falsity write by Nils Kürbis. This book was released on 2019-05-09. Proof and Falsity available in PDF, EPUB and Kindle. Provides an original analysis of negation - a central concept of logic - and how to define its meaning in proof-theoretic semantics.
