The Mathematical Analysis of Logic
Author: George Boole
Publisher:
Published: 1847
Total Pages: 94
ISBN-13:
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Mathematical Logic through Python
Author: Yannai A. Gonczarowski
Publisher: Cambridge University Press
Published: 2022-07-31
Total Pages: 286
ISBN-13: 1108957692
DOWNLOAD EBOOKUsing a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.
The Mathematical Analysis of Logic
Author: George Boole
Publisher:
Published: 1847
Total Pages: 330
ISBN-13:
DOWNLOAD EBOOKTopoi
Author: R. Goldblatt
Publisher: Elsevier
Published: 2014-06-28
Total Pages: 569
ISBN-13: 148329921X
DOWNLOAD EBOOKThe 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, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.
An Investigation of the Laws of Thought
Author: George Boole
Publisher:
Published: 1854
Total Pages: 450
ISBN-13:
DOWNLOAD EBOOKMathematical Analysis and Proof
Author: David S G Stirling
Publisher: Horwood Publishing
Published: 2009-05-14
Total Pages: 266
ISBN-13: 9781904275404
DOWNLOAD EBOOKThis fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which users have indicated a need for, in addition to more emphasis on how analysis can be used to tell the accuracy of the approximations to the quantities of interest which arise in analytical limits. Addresses a lack of familiarity with formal proof, a weakness observed among present-day mathematics students Examines the idea of mathematical proof, the need for it and the technical and logical skills required
Mathematical Logic
Author: H.-D. Ebbinghaus
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 290
ISBN-13: 1475723555
DOWNLOAD EBOOKThis introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
The Mathematical Analysis of Logic
Author: George Boole
Publisher: Cambridge University Press
Published: 2009-07-20
Total Pages: 95
ISBN-13: 1108001017
DOWNLOAD EBOOKIn The Mathematical Analysis of Logic, mathematician George Boole persuasively argues that logic should be aligned with mathematics, not philosophy.
A Tour Through Mathematical Logic
Author: Robert S. Wolf
Publisher: American Mathematical Soc.
Published: 2005-12-31
Total Pages: 414
ISBN-13: 161444028X
DOWNLOAD EBOOKA Tour Through Mathematical Logic provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory.
Algebraic Logic
Author: Semen Grigorʹevich Gindikin
Publisher: Springer Science & Business Media
Published: 1985-10-14
Total Pages: 386
ISBN-13: 9780387961798
DOWNLOAD EBOOKThe popular literature on mathematical logic is rather extensive and written for the most varied categories of readers. College students or adults who read it in their free time may find here a vast number of thought-provoking logical problems. The reader who wishes to enrich his mathematical background in the hope that this will help him in his everyday life can discover detailed descriptions of practical (and quite often -- not so practical!) applications of logic. The large number of popular books on logic has given rise to the hope that by applying mathematical logic, students will finally learn how to distinguish between necessary and sufficient conditions and other points of logic in the college course in mathematics. But the habit of teachers of mathematical analysis, for example, to stick to problems dealing with sequences without limit, uniformly continuous functions, etc. has, unfortunately, led to the writing of textbooks that present prescriptions for the mechanical construction of definitions of negative concepts which seem to obviate the need for any thinking on the reader's part. We are most certainly not able to enumerate everything the reader may draw out of existing books on mathematical logic, however.
