476,64 zł

Mathematical Logic Springer International Publishing AG

Książki / Literatura obcojęzyczna

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions.Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments.The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures.The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

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360,97 zł

Mathematical Logic Springer Nature Switzerland AG

Książki / Literatura obcojęzyczna

This 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 Fra

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285,10 zł

Mathematical Logic Springer Nature Switzerland AG

Książki / Literatura obcojęzyczna

This 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 Fra

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125,21 zł

Introduction to Mathematical Logic Dover Publications Inc.

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Preface 1. Background 2. Language and Semantics of Propositional Logic 3. Propositional Logic 4. First-Order Languages 5. First-Order Logic 6. Mathematics and Logic 7. Incompleteness, Undecidability and Indefinability 8. Recursive Functions 9. Compatability Theory 10. Hilbert's Tenth Problem Appendix: Number Theory References and recommended readings Index

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664,47 zł

Introduction to Mathematical Logic Apple Academic Press Inc.

Książki / Literatura obcojęzyczna

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, an

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227,92 zł

Introduction to Mathematical Logic World Scientific Publishing

Książki / Literatura obcojęzyczna

This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book does not presuppose any previous knowledge and can be used also for self-study by more ambitious students. Starting with the basics of set theory, induction and computability, it covers propositional and first-order logic - their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts. Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules - of a high, though often neglected, pedagogical value - aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, in which careful presentation of concepts, results and examples is accompanied by the informal analogies and illustrations. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of mathematical logic.

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150,84 zł

Handbook of Mathematical Fuzzy Logic. Volume 1 College Publications

Książki / Literatura obcojęzyczna

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers.This two-volume handbook provides an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, who may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. Despite being located in the realm of pure mathematical logic, this handbook will also be useful for readers interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness.The first volume contains a gentle introduction to MFL, a presentation of an abstract algebraic framework for MFL, chapters on proof theory and algebraic semantics of fuzzy logics, and, fi nally, an algebraic study of Hájek's logic BL. The second volume is devoted to Lukasiewicz logic and MValgebras, Gödel-Dummett logic and its variants, fuzzy logics in expanded propositional languages, studies of functional representations for fuzzy logics and their free algebras, computational complexity of propositional logics, and arithmetical complexity of first-order logics.

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374,84 zł

Mathematical Logic Springer Nature Switzerland AG

Książki / Literatura obcojęzyczna

This book gathers together a colorful set of problems on classical Mathematical Logic, selected from over 30 years of teaching. The initial chapters start with problems from supporting fields, like set theory (ultrafilter constructions), full-information game theory (strategies), automata, and recursion theory (decidability, Kleene's theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht- Fra

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350,92 zł

Beginner's Further Guide To Mathematical Logic, A World Scientific Publishing Co Pte Ltd

Książki / Literatura obcojęzyczna

This is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a

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128,42 zł

Beginner's Further Guide To Mathematical Logic, A World Scientific Publishing Co Pte Ltd

Książki / Literatura obcojęzyczna

This is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a

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65,21 zł

Introduction to Logic Dover Publications Inc.

Książki / Literatura obcojęzyczna

PREFACEFROM THE PREFACE TO THE ORIGINAL EDITIONFIRST PART ELEMENTS OF LOGIC. DEDUCTIVE METHODI. ON THE USE OF VARIABLES 1. Constants and variables 2. Expressions containing variables-sentential and designatory functions 3. Formation of sentences by means of variables-universal and existential sentences 4. Universal and existential quantifiers; free and bound variables 5. The importance of variables in mathematics ExercisesII. ON THE SENTENTIAL CALCULUS 6. Logical constants; the old logic and the new logic 7. "Sentential calculus; negation of a sentence, conjunction and disjunction of sentences" 8. Implication or conditional sentence; implication in material meaning 9. The use of implication in mathematics 10. Equivalence of sentences 11. The formulation of definitions and its rules 12. Laws of sentential calculus 13. Symbolism of sentential calculus; truth functions and truth tables 14. Application of laws of sentential calculus in inference 15. "Rules of inference, complete proofs" ExercisesIII. ON THE THEORY OF IDENTITY 16. Logical concepts outside sentential calculus; concept of identity 17. Fundamental laws of the theory of identity 18. Identity of things and identity of their designations; use of quotation marks 19. "Equality in arithmetic and geometry, and its relation to logical identity" 20. Numerical quantifiers ExercisesIV. ON THE THEORY OF CLASSES 21. Classes and their elements 22. Classes and sentential functions with one free variable 23. Universal class and null class 24. Fundamental relations among classes 25. Operations on classes 26. "Equinumerous classes, cardinal number of a class, finite and infinite classes; arithmetic as a part of logic" ExercisesV. ON THE THEORY OF RELATIONS 27. "Relations, their domains and counter-domains; relations and sentential functions with two free variables" 28. Calculus of relations 29. Some properties of relations 30 "Relations which are reflexive, symmetrical and transitive" 31. Ordering relations; examples of other relations 32. One-many relations or functions 33. "One-one relations or biunique functions, and one-to-one correspondences" 34. Many-termed relations; functions of several variables and operations 35. The importance of logic for other sciences ExercisesVI. ON THE DEDUCTIVE METHOD 36. "Fundamental constituents of a deductive theory-primitive and defined terms, axioms and theorems" 37. Model and interpretation of a deductive theory 38. Law of deduction; formal character of deductive sciences 39. Selection of axioms and primitive terms; their independence 40. "Formalization of definitions and proofs, formalized deductive theories" 41. Consistency and completeness of a deductive theory; decision problem 42. The widened conception of the methodology of deductive sciences ExercisesSECOND PART APPLICATIONS OF LOGIC AND METHODOLOGY IN CONSTRUCTING MATHEMATICAL THEORIESVII. CONSTRUCTION OF A MATHEMATICAL THEORY: LAWS OF ORDER FOR NUMBERS 43. Primitive terms of the theory under construction; axioms concerning fundamental relations among numbers 44. Laws of irreflexivity for the fundamental relations; indirect proofs 45. Further theorems on the fundamental relations 46. Other relations among numbers ExercisesVIII. CONSTRUCTION OF A MATHEMATICAL THEORY: LAWS OF ADDITION AND SUBTRACTION 47. "Axioms concerning addition; general properties of operations, concepts of a group and of an Abelian group" 48. Commutative and associative laws for a larger number of summands 49. Laws of monotony for addition and their converses 50. Closed systems of sentences 51. Consequences of the laws of monotony 52. Definition of subtraction; inverse operations 53. Definitions whose definiendum contains the identity sign 54. Theorems on subtraction ExercisesIX. METHODOLOGICAL CONSIDERATIONS ON THE CONSTRUCTED THEORY 55. Elimination of superfluous axioms in the original axiom system 56. Independence of the axioms of the simplified system 57. Elimination of superfluous primitive terms and subsequent simplification of the axiom system; concept of an ordered Abelian group 58. Further simplification of the axiom system; possible transformations of the system of primitive terms 59. Problem of the consistency of the constructed theory 60. Problem of the completeness of the constructed theory ExercisesX. EXTENSION OF THE CONSTRUCTED THEORY. FOUNDATIONS OF ARITHMETIC OF REAL NUMBERS 61. First axiom system for the arithmetic of real numbers 62. Closer characterization of the first axiom system; its methodological advantages and didactical disadvantages 63. Second axiom system for the arithmetic of real numbers 64. Closer characterization of the second axiom system; concepts of a field and of an ordered field 65. Equipollence of the two axiom systems; methodological disadvantages and didactical advantages of the second system ExercisesSUGGESTED READINGSINDEX

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935,89 zł

Matrix Logic and Mind North-Holland

Książki / Literatura obcojęzyczna

In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields. In the field of fundamental physics, the author reaches the revolutionary conclusion that physics can be viewed and studied as logic in a fundamental sense, as compared with Einstein's view of physics as space-time geometry. This opens new, exciting prospects for the study of fundamental interactions. A formulation of logic in terms of matrix operators and logic vector spaces allows the author to tackle for the first time, the intractable problem of cognition in a scientific manner.In the same way as the findings of Heisenberg and Dirac in the 1930s provided a conceptual and mathematical foundation for quantum physics, matrix operator logic supports an important breakthrough in the study of the physics of the mind, which is interpreted as a fractal of quantum mechanics. Introducing a concept of logic quantum numbers, the author concludes that the problem of logic and the intelligence code in general can be effectively formulated as eigenvalue problems similar to those of theoretical physics. With this important leap forward in the study of the mechanism of mind, the author concludes that the latter cannot be fully understood either within classical or quantum notions. A higher-order covariant theory is required to accommodate the fundamental effect of high-level intelligence. The landmark results obtained by the author will have implications and repercussions for the very foundations of science as a whole. Moreover, Stern's "Matrix Logic" is suitable for a broad spectrum of practical applications in contemporary technologies.

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75,56 zł

Algebraic Logic Martino Fine Books

Książki / Literatura obcojęzyczna

2014 Reprint of 1962 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In "Algebraic Logic" Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra. This book addresses some of the problems of mathematical logic and the theory of polyadic Boolean algebras in particular. It is intended to be an efficient way of treating algebraic logic in a unified manner.

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293,24 zł

Basic Proof Theory Cambridge University Press

Książki / Literatura obcojęzyczna

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.

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104,51 zł

All about Proofs, Proofs for All College Publications

Książki / Literatura obcojęzyczna

The development of new and improved proof systems, proof formats andproof search methods is one of the most essential goals of Logic. Butwhat is a proof? What makes a proof better than another? How can aproof be found efficiently? How can a proof be used? Logicians fromdifferent communities usually provide radically different answers tosuch questions. Their principles may be folklore within their owncommunities but are often unknown to outsiders.This book provides a snapshot of the current state of the art in proofsearch and proof production as implemented in contemporary automatedreasoning tools such as SAT-solvers, SMT-solvers, first-order andhigher-order automated theorem provers and proof assistants.Furthermore, various trends in proof theory, such as the calculus ofinductive constructions, deduction modulo, deep inference,foundational proof certificates and cut-elimination, are surveyed;and applications of formal proofs are illustrated in the areas ofcryptography, verification and mathematical proof mining.Experts in these topics were invited to present tutorials about proofsduring the Vienna Summer of Logic and the chapters in this bookreflect their tutorials. Therefore, each chapter is intended to beaccessible not only to experts but also to novice researchersfrom all fields of Logic.

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