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Language, Truth and Logic in Mathematics

Posted By: AvaxGenius
Date: 9 Jul 2022 18:47:11
Language, Truth and Logic in Mathematics

Language, Truth and Logic in Mathematics by Jaakko Hintikka
English | PDF | 1998 | 257 Pages | ISBN : 0792347668 | 26.8 MB

One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer.
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Logic and Structure

Posted By: AvaxGenius
Date: 9 Jul 2022 14:36:15
Logic and Structure

Logic and Structure, Third Edition by Dirk Dalen
English | PDF | 1994 | 225 Pages | ISBN : 3540578390 | 17.8 MB

A book which efficiently presents the basics of propositional and predicate logic, van Dalen’s popular textbook contains a complete treatment of elementary classical logic, using Gentzen’s Natural Deduction. Propositional and predicate logic are treated in separate chapters in a leisured but precise way. Chapter Three presents the basic facts of model theory, e.g. compactness, Skolem-Löwenheim, elementary equivalence, non-standard models, quantifier elimination, and Skolem functions.
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Logic and Structure

Posted By: AvaxGenius
Date: 9 Jul 2022 14:31:52
Logic and Structure

Logic and Structure by Dirk Dalen
English | PDF | 1980 | 182 Pages | ISBN : 3540098933 | 11.4 MB

A book which efficiently presents the basics of propositional and predicate logic, van Dalen’s popular textbook contains a complete treatment of elementary classical logic, using Gentzen’s Natural Deduction. Propositional and predicate logic are treated in separate chapters in a leisured but precise way. Chapter Three presents the basic facts of model theory, e.g. compactness, Skolem-Löwenheim, elementary equivalence, non-standard models, quantifier elimination, and Skolem functions.
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Logic for Computer Scientists

Posted By: AvaxGenius
Date: 20 Jul 2021 06:45:24
Logic for Computer Scientists

Logic for Computer Scientists by Uwe Schöning
English | PDF | 2008 | 172 Pages | ISBN : 0817634533 | 10.1 MB

This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way.
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A Short Introduction to Intuitionistic Logic

Posted By: AvaxGenius
Date: 6 Jul 2021 12:08:37
A Short Introduction to Intuitionistic Logic

A Short Introduction to Intuitionistic Logic by Grigori Mints
English | PDF | 2000 | 130 Pages | ISBN : 0306463946 | 15.6 MB

Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs.
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Problems in Set Theory, Mathematical Logic and the Theory of Algorithms

Posted By: AvaxGenius
Date: 30 Jun 2021 08:35:57
Problems in Set Theory, Mathematical Logic and the Theory of Algorithms

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by Igor Lavrov
English | PDF | 2003 | 288 Pages | ISBN : 0306477122 | 16.9 MB

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.
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Superminds: People Harness Hypercomputation, and More

Posted By: AvaxGenius
Date: 26 May 2020 22:24:45
Superminds: People Harness Hypercomputation, and More

Superminds: People Harness Hypercomputation, and More by Selmer Bringsjord
English | PDF,EPUB | 2003 | 368 Pages | ISBN : 140201094X | 54.2 MB

This is the first book-length presentation and defense of a new theory of human and machine cognition, according to which human persons are superminds. Superminds are capable of processing information not only at and below the level of Turing machines (standard computers), but above that level (the "Turing Limit"), as information processing devices that have not yet been (and perhaps can never be) built, but have been mathematically specified; these devices are known as super-Turing machines or hypercomputers.
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