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Provability, Computability and Reflection

Syllogism --- Modality (Logic) --- Syllogisme --- Modalité (Logique) --- Aristotle. --- EPUB-LIV-FT ELSEVIER-B --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- Modality (Logic). --- Syllogism.

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This book presents the first study of the development of the theory of modal syllogistic in the Middle Ages. It traces the theory from the first medieval commentators on Aristotle's Prior Analytics to the end of the Middle Ages. In the book, several previously unstudied texts are analysed and the works of philosophers like Robert Kilwardby, Albert the Great, Richard of Campsall, William of Ockham, John Buridan, Pseudo-Scotus, Albert of Saxony, Marsilius of Inghen and Jodocus Trutfetter are studied. These authors' views on modal syllogistics are shown to comprise important insights clarifying central issues with implications for medieval philosophy in general. The book will be of particular interest to historians of medieval philosophy and logic, but also to anyone interested in the history of logic and Aristotelian philosophy.

Logic [Medieval ] --- Logica [Middeleeuwse ] --- Logique médiévale --- Medieval logic --- Middeleeuwse logica --- Syllogism --- Modality (Logic) --- Logic, Medieval --- Syllogisme --- Modalité (Logique) --- History --- Histoire --- Logic, Medieval. --- 510.64 --- 162.2 --- -Syllogism --- -Argumentation --- Logic --- Reasoning --- Logic, Symbolic and mathematical --- Modal logic --- Nonclassical mathematical logic --- Bisimulation --- Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- Syllogisme. Deductie --- -History --- -510.64 --- -Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- 162.2 Syllogisme. Deductie --- 510.64 Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- -Medieval logic --- Argumentation --- Modalité (Logique) --- Logique médiévale --- To 1500 --- Syllogism - History - To 1500. --- Modality (Logic) - History - To 1500.

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Simplicity theory is an extension of stability theory to a wider class of structures, containing, among others, the random graph, pseudo-finite fields, and fields with a generic automorphism. Following Kim's proof of `forking symmetry' which implies a good behaviour of model-theoretic independence, this area of model theory has been a field of intense study. It has necessitated the development of some important new tools, most notably the model-theoretic treatment of hyperimaginaries (classes modulo type-definable equivalence relations). It thus provides a general notion of independence (and of rank in the supersimple case) applicable to a wide class of algebraic structures. The basic theory of forking independence is developed, and its properties in a simple structure are analyzed. No prior knowledge of stability theory is assumed; in fact many stability-theoretic results follow either from more general propositions, or are developed in side remarks. Audience: This book is intended both as an introduction to simplicity theory accessible to graduate students with some knowledge of model theory, and as a reference work for research in the field.

Model theory. --- Théorie des modèles --- Model theory --- Théorie des modèles --- Mathematical logic. --- Group theory. --- Commutative algebra. --- Commutative rings. --- Mathematical Logic and Foundations. --- Group Theory and Generalizations. --- Commutative Rings and Algebras. --- Rings (Algebra) --- Algebra --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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I am very happy to have this opportunity to introduce Luca Vigano's book on Labelled Non-Classical Logics. I put forward the methodology of labelled deductive systems to the participants of Logic Colloquium'90 (Labelled Deductive systems, a Position Paper, In J. Oikkonen and J. Vaananen, editors, Logic Colloquium '90, Volume 2 of Lecture Notes in Logic, pages 66-68, Springer, Berlin, 1993), in an attempt to bring labelling as a recognised and significant component of our logic culture. It was a response to earlier isolated uses of labels by various distinguished authors, as a means to achieve local proof­ theoretic goals. Labelling was used in many different areas such as resource labelling in relevance logics, prefix tableaux in modal logics, annotated logic programs in logic programming, proof tracing in truth maintenance systems, and various side annotations in higher-order proof theory, arithmetic and analysis. This widespread local use of labels was an indication of an underlying logical pattern, namely the simultaneous side-by-side manipulation of several kinds of logical information. It was clear that there was a need to establish the labelled deductive systems methodology. Modal logic is one major area where labelling can be developed quickly and sys­ tematically with a view of demonstrating its power and significant advantage. In modal logic the labels can play a double role.

Nonclassical mathematical logic. --- Logic. --- Computer science. --- Mathematical logic. --- Computer Science, general. --- Mathematical Logic and Foundations. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Informatics --- Science --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Reasoning --- Thought and thinking --- Methodology

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Logic, Symbolic and mathematical --- Logique symbolique et mathématique --- EPUB-LIV-FT ELSEVIER-B --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism