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The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics,

Mathematical logic --- Toposes. --- Topoi (Mathematics) --- Categories (Mathematics) --- Toposes

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This open access book investigates the role played by identity of proofs in proof-theoretic semantics. It develops a conception of proof-theoretic semantics as primarily concerned with the relationship between proofs (understood as abstract entities) and derivations (the linguistic representations of proofs). It demonstrates that identity of proof is a key both to clarify some —still not wholly understood— notions at the core of proof-theoretic semantics, such as harmony; and to broaden the range of the phenomena which can be analyzed using the tools of this semantic paradigm, so as to include for instance paradoxes. The volume covers topics such as the philosophical significance of different criteria of identity of proofs, and adequacy conditions for an intensional account of the notion of harmony. The author also examines the Prawitz-Tennant analysis of paradoxes by investigating on the one hand the prospects of turning it into a theory of meaning for paradoxical languages, and on the other hand two distinct kinds of phenomena, first observed by Crabbe and Ekman, showing that the Tennant-Prawitz criterion for paradoxicality overgenerates. This volume is of interest to scholars in formal and philosophical logic.

Logic. --- Machine theory. --- Mathematical logic. --- Formal Languages and Automata Theory. --- Mathematical Logic and Foundations. --- Logic, Symbolic and mathematical.

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This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. The chapters of which this book is composed discuss the subject from a rich variety of angles, including the history of logic, the proper interpretation of logical validity, natural deduction rules, the notions of harmony and of synonymy, the structure of proofs, the logical status of equality, intentional phenomena, and the proof theory of second-order arithmetic. All chapters relate directly to questions that have driven Schroeder-Heister's own research agenda andto which he has made seminal contributions. The extensive autobiographical chapter not only provides a fascinating overview of Schroeder-Heister's career and the evolution of his academic interests but also constitutes a contribution to the recent history of logic in its own right, painting an intriguing picture of the philosophical, logical, and mathematical institutional landscape in Germany and elsewhere since the early 1970s. The papers collected in this book are illuminatingly put into a unified perspective by Schroeder-Heister's comments at the end of the book. Both graduate students and established researchers in the field will find this book an excellent resource for future work in proof-theoretic semantics and related areas.

Philosophy. --- Logic. --- Language and languages --- Mathematics --- Mathematical logic. --- Linguistics. --- Philosophy of Language. --- Philosophy of Mathematics. --- Mathematical Logic and Foundations. --- Logic, Symbolic and mathematical.

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The Bulletin of Symbolic Logic was established in 1995 by the Association for Symbolic Logic (ASL) to provide a journal of high standards that would be both accessible and of interest to as wide an audience as possible. Its stated purpose is to keep the logic community informed quickly of important developments in all parts of the discipline. The Bulletin of Symbolic Logic primarily publishes two types of papers: articles and communications. Articles present topics of broad interest that should be accessible to a large audience. They can be purely expository, survey, or historical articles, or they may contain, in addition, new ideas or results or new approaches to old ones. Communications are announcements of important new results and ideas. They are expected to include a description of the new work, as well as enough history, background, and explanation to make the significance of the work apparent to a wide audience. Papers in The Bulletin may deal with any aspect of logic, including mathematical or philosophical logic, logic in computer science or linguistics, the history or philosophy of logic, or applications of logic to other fields.

Logic, Symbolic and mathematical --- JEX4 --- Logique symbolique et mathématique --- Logic, Symbolic and mathematical. --- Symbolische logica. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Lògica. --- Lògica matemàtica.

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This open access book constitutes the proceedings of the First International Conference on Robust Argumentation Machines, RATIO 2024, which took place in Bielefeld, Germany, during June 5-7, 2024. The 20 full papers and 1 short paper included in the proceedings were carefully reviewed and selected from 24 submissions. They were organized in topical sections as follows: Argument Mining; Debate Analysis and Deliberation; Argument Acquisition, Annotation and Quality Assessment; Computational Models of Argumentation; Interactive Argumentation, Recommendation and Personalization; and Argument Search and Retrieval. .

Artificial intelligence. --- Computer science. --- Logic programming. --- Mathematical logic. --- Machine theory. --- Software engineering. --- Artificial Intelligence. --- Theory of Computation. --- Logic in AI. --- Mathematical Logic and Foundations. --- Formal Languages and Automata Theory. --- Software Engineering. --- Logic, Symbolic and mathematical.