pure inductive logic perspectives in logic

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Pure Inductive Logic

Author : Jeffrey Paris
ISBN : 9781316393079
Genre : Mathematics
File Size : 39. 66 MB
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Pure inductive logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years plus the main contributions of the authors and their collaborators over the last decade to present a comprehensive account of the discipline within a single unified context. The exposition is structured around the traditional bases of rationality, such as avoiding Dutch Books, respecting symmetry and ignoring irrelevant information. The authors uncover further rationality concepts, both in the unary and in the newly emerging polyadic languages, such as conformity, spectrum exchangeability, similarity and language invariance. For logicians with a mathematical grounding, this book provides a complete self-contained course on the subject, taking the reader from the basics up to the most recent developments. It is also a useful reference for a wider audience from philosophy and computer science.

Logic Without Borders

Author : Åsa Hirvonen
ISBN : 9781614516873
Genre : Philosophy
File Size : 34. 22 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.

Rudolf Carnap Logical Empiricist

Author : Jaakko Hintikka
ISBN : 9789401018074
Genre : Science
File Size : 61. 48 MB
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Inductive Logic Programming

Author : Stephen Muggleton
ISBN : 9783540738466
Genre : Computers
File Size : 85. 7 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 : 56. 15 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.

Abduction And Induction

Author : P.A. Flach
ISBN : 0792362500
Genre : Computers
File Size : 23. 50 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.

Informal Fallacies

Author : Douglas N. Walton
ISBN : 9789027250056
Genre : Philosophy
File Size : 25. 27 MB
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The basic question of this monograph is: how should we go about judging arguments to be reasonable or unreasonable? Our concern will be with argument in a broad sense, with realistic arguments in natural language. The basic object will be to engage in a normative study of determining what factors, standards, or procedures should be adopted or appealed to in evaluating an argument as “good,” “not-so-good,” “open to criticism,” “fallacious,” and so forth. Hence our primary concern will be with the problems of how to criticize an argument, and when a criticism is reasonably justified.

Lambda Calculus With Types

Author : Henk Barendregt
ISBN : 9781107276345
Genre : Mathematics
File Size : 86. 97 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.

Logic In Reality

ISBN : 9781402083754
Genre : Philosophy
File Size : 40. 22 MB
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This book is both dif?cult and rewarding, affording a new perspective on logic and reality, basically seen in terms of change and stability, being and becoming. Most importantly it exemplifies a mode of doing philosophy of science that seems a welcome departure from the traditional focus on purely analytic arguments. The author approaches ontology, metaphysics, and logic as having offered a number of ways of constructing the description of reality, and aims at deepening their relationships in a new way. Going beyond the mere abstract and formal aspects of logical analysis, he offers a new architecture of logic that sees it as applied not only to the “reasoning processes” belonging to the first disciplinary group – ontology – but also directly concerned with en- ties, events, and phenomena studied by the second one – metaphysics. It is the task of the book to elaborate such a constructive logic, both by offering a lo- cal view of the structure of the reality in general and by proffering a wealth of models able to encompass its implications for science. In turning from the merely formal to the constructive account of logic Brenner overcomes the limitation of logic to linguistic concepts so that it can be not only a logic “of” reality but also “in” that reality which is constitutively characterized by a number of fundamental dualities (observer and observed, self and not-self, internal and external, etc.

Applications Of Inductive Logic

Author : Laurence Jonathan Cohen
ISBN : UOM:39015000528300
Genre : Induction (Logic)
File Size : 61. 7 MB
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