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Nonclassical mathematical logic --- Logique mathématique non classique --- Nonclassical mathematical logic. --- Mathematical logic, Nonclassical --- Non-classical mathematical logic --- Logic, Symbolic and mathematical --- Logique mathématique non classique

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Differential equations, Parabolic. --- Nonclassical mathematical logic. --- Inverse problems (Differential equations) --- Numerical analysis. --- Mathematical analysis --- Differential equations --- Mathematical logic, Nonclassical --- Non-classical mathematical logic --- Logic, Symbolic and mathematical --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial

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This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

Nonclassical mathematical logic --- Logique mathématique non classique --- Nonclassical mathematical logic. --- Logique mathématique non classique --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Mathematical logic, Nonclassical --- Non-classical mathematical logic --- Logic, Symbolic and mathematical --- Arts and Humanities --- Philosophy --- Logique --- Logique propositionnelle --- 20e siècle --- Lògica matemàtica

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Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

Proof theory --- Computable functions --- Nonclassical mathematical logic --- Nichtklassische Logik. --- Beweistheorie. --- Berechenbarkeit. --- Proof theory. --- Nonclassical mathematical logic. --- Computable functions. --- Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Constructive mathematics --- Decidability (Mathematical logic) --- Mathematical logic, Nonclassical --- Non-classical mathematical logic --- Logic, Symbolic and mathematical --- Rekursionstheorie --- Berechnungstheorie --- Transklassische Logik --- Logik --- Klassische Logik

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Analytic philosophy has leveled many challenges to Kant's ascription of necessary properties and relations to objects in his Critique of Pure Reason. Some of these challenges can be answered, it is argued here, largely in terms of techniques belonging to analytic philosophy itself, in particular, to its philosophy of language. This Kantian response is the primary objective of this book. It takes the form of a compromise between the real existence of the objects that we can intuit and that get our knowledge started - dubbed initiators - and the ideality of the necessary properties and relations that Kant ascribes to our sensible representations of initiators, which he entitles appearances. Whereas the real existence of initiators is independent of us and our senses, the necessity of these properties and relations of appearances is due to their origins in the mind. The Kantian compromise between real existence and ideal necessity is formulated in terms of David Kaplan's interpretation of de re necessity in his article, "Quantifying In" - his response to Quine's concern that a commitment to such a necessity leads to an acceptance of an unwanted traditional Aristotelian essentialism. In addition, the book first abstracts and then departs from its interpretation of Kant to provide a realistic account of the relation between existence and de re necessity.

Modality (Logic) --- Knowledge, Theory of --- Nonclassical mathematical logic. --- Mathematical logic, Nonclassical --- Non-classical mathematical logic --- Logic, Symbolic and mathematical --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation --- History --- History. --- Kant, Immanuel, --- Kant, Immanuel --- Kant, I. --- Kānt, ʻAmmānūʼīl, --- Kant, Immanouel, --- Kant, Immanuil, --- Kʻantʻŭ, --- Kant, --- Kant, Emmanuel, --- Ḳanṭ, ʻImanuʼel, --- Kant, E., --- Kant, Emanuel, --- Cantơ, I., --- Kant, Emanuele, --- Kant, Im. --- קאנט --- קאנט, א. --- קאנט, עמנואל --- קאנט, עמנואל, --- קאנט, ע. --- קנט --- קנט, עמנואל --- קנט, עמנואל, --- كانت ، ايمانوئل --- كنت، إمانويل، --- カントイマニユエル, --- Kangde, --- 康德, --- Kanṭ, Īmānwīl, --- كانط، إيمانويل --- Kant, Manuel, --- Existence. --- Kant, Imanuel. --- Knowledge. --- Logic. --- Necessity.