pure inductive logic perspectives in logic

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Pure Inductive Logic

Author : Jeffrey Paris
ISBN : 9781107042308
Genre : Computers
File Size : 23. 45 MB
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A self-contained guide to pure inductive logic, the study of rational probability treated as a branch of mathematical logic.

Logic Without Borders

Author : Åsa Hirvonen
ISBN : 9781614516873
Genre : Philosophy
File Size : 32. 11 MB
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In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

Inductive Logic Programming

Author : Stephen Muggleton
ISBN : 9783540738466
Genre : Computers
File Size : 64. 42 MB
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This book constitutes the thoroughly refereed post-proceedings of the 16th International Conference on Inductive Logic Programming, ILP 2006, held in Santiago de Compostela, Spain, in August 2006.The 27 revised full papers presented together with 5 invited papers and the extended abstracts of 7 special issue papers were carefully reviewed and selected from 77 initial submissions. The papers address all current topics in inductive logic programming, ranging from theoretical and methodological issues to advanced applications in various areas, thus presenting original results on all aspects of learning in logic, as well as multi-relational data mining and learning, statistical relational learning, graph and tree mining, and learning in other (non-propositional) logic-based knowledge representation frameworks.

Proofs And Computations

Author : Helmut Schwichtenberg
ISBN : 9781139504164
Genre : Mathematics
File Size : 72. 85 MB
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Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.

Metamathematics Of First Order Arithmetic

Author : Petr Hájek
ISBN : 9781316739457
Genre : Mathematics
File Size : 24. 20 MB
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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

Lambda Calculus With Types

Author : Henk Barendregt
ISBN : 9781107276345
Genre : Mathematics
File Size : 39. 50 MB
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This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.

Applications Of Inductive Logic

Author : Laurence Jonathan Cohen
ISBN : UOM:39015000528300
Genre : Induction (Logic)
File Size : 47. 33 MB
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A Computational Logic

Author : Robert S. Boyer
ISBN : OCLC:606031734
Genre :
File Size : 42. 15 MB
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Abduction And Induction

Author : P.A. Flach
ISBN : 0792362500
Genre : Computers
File Size : 54. 92 MB
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From the very beginning of their investigation of human reasoning, philosophers have identified two other forms of reasoning, besides deduction, which we now call abduction and induction. Deduction is now fairly well understood, but abduction and induction have eluded a similar level of understanding. The papers collected here address the relationship between abduction and induction and their possible integration. The approach is sometimes philosophical, sometimes that of pure logic, and some papers adopt the more task-oriented approach of AI. The book will command the attention of philosophers, logicians, AI researchers and computer scientists in general.

Higher Recursion Theory

Author : Gerald E. Sacks
ISBN : 9781107168435
Genre : Mathematics
File Size : 41. 85 MB
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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, α-recursion, and E-recursion. This text is essential reading for all researchers in the field.

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