Proof Complexity and Feasible Arithmetics

Author: Paul W. Beame
Publisher: American Mathematical Soc.
ISBN: 0821870823
Release Date:
Genre: Mathematics

Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether or not logical inferences can be made but also what resources are required to carry them out. Understanding the resources required for logical inferences has major implications for some of the most important problems in computational complexity, particularly the problem of whether or not NP is equal to co-NP. In addition, these have important implications for the efficiency of automated reasoning systems. The last dozen years have seen several breakthroughs in the study of these resource requirement. Papers in this volume represent the proceedings of the DIMACS workshop on "Feasible Arithmetics and Proof Complexity" held in April 1996 in Rutgers, NJ, as part of the DIMACS Institute's Special Year on Logic and Algorithms. This book brings together some of the most recent work of leading researchers in proof complexity and feasible arithmetic reflecting many of these advances. It covers a number of aspects of the field including lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, interpolation theorems, and the relationship between proof complexity and Boolean circuit complexity.

Truth in Mathematics

Author: Harold G. Dales
Publisher: Oxford University Press
ISBN: 019851476X
Release Date: 1998
Genre: Mathematics

The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. This book is an overview of the most recent work undertaken in this subject, and is unique in being the result of interactions between researchers from both philosophy and mathematics. The articles are written by world leaders in their respective fields and are of interest to researchers in both disciplines.

Introduction to Mathematical Logic Fourth Edition

Author: Elliott Mendelson
Publisher: CRC Press
ISBN: 0412808307
Release Date: 1997-06-01
Genre: Mathematics

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

AI IA 99 Advances in Artificial Intelligence

Author: Associazione italiana per l'intelligenza artificiale. Congress
Publisher: Springer Science & Business Media
ISBN: 9783540673507
Release Date: 2000-03-29
Genre: Computers

This book constitutes the thoroughly refereed post-conference proceedings of the 6th Congress of the Italian Association for Artificial Intelligence, AI*IA 99, held in Bologna, Italy, in September 1999. The 33 revised full papers presented were carefully reviewed and selected for inclusion in the book from a total of 64 congress submissions. The papers are organized in topical sections on knowledge representation; automated reasoning; temporal and qualitative reasoning; machine learning, data mining, and theory revision; natural language processing and web interfaces; multi-agent systems; perception and robotics; and planning and scheduling.

Computability

Author: Richard L. Epstein
Publisher: Chapman and Hall/CRC
ISBN: 0534103561
Release Date: 1989-11-09
Genre: Mathematics

An introduction to recursion theory and particularly to the theory of computing, including fourteen readings by Hilbert, Godel, Turing, Post, Church, and others along with a discussion of issues such as self-reference and infinite sets. Annotation copyrighted by Book News, Inc., Portland, OR

Classical Mathematical Logic

Author: Richard L. Epstein
Publisher: Princeton University Press
ISBN: 9781400841554
Release Date: 2011-12-18
Genre: Mathematics

In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.

Modality

Author: Joseph Melia
Publisher: Routledge
ISBN: 9781317489689
Release Date: 2014-12-18
Genre: Philosophy

This introduction to modality places the emphasis on the metaphysics of modality rather than on the formal semetics of quantified modal logic. The text begins by introducing students to the "de re/de dicto" distinction, conventionalist and conceptualist theories of modality and some of the key problems in modality, particularly Quine's criticisms. It then moves on to explain how possible worlds provide a solution to many of the problems in modality and how possible worlds themselves have been used to analyse notions outside modality such as properties and propositions. Possible worlds introduce problems of their own and the book argues that to make progress with these problems a theory of possible worlds is required. The pros and cons of various theories of possible worlds are then examined in turn, including those of Lewis, Kripke, Adams, Stalnaker and Plantinga.

AI IA 99 Advances in Artificial Intelligence

Author: Evelina Lamma
Publisher: Springer
ISBN: UOM:39015047800795
Release Date: 2000-05-11
Genre: Artificial intelligence

This book constitutes the thoroughly refereed post-conference proceedings of the 6th Congress of the Italian Association for Artificial Intelligence, AI*IA 99, held in Bologna, Italy, in September 1999. The 33 revised full papers presented were carefully reviewed and selected for inclusion in the book from a total of 64 congress submissions. The papers are organized in topical sections on knowledge representation; automated reasoning; temporal and qualitative reasoning; machine learning, data mining, and theory revision; natural language processing and web interfaces; multi-agent systems; perception and robotics; and planning and scheduling.

Lingua Universalis vs Calculus Ratiocinator

Author: Jaakko Hintikka
Publisher: Springer Science & Business Media
ISBN: 9789401586016
Release Date: 2013-04-09
Genre: Philosophy

R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however.

Counterexamples in Probability And Statistics

Author: A.F. Siegel
Publisher: Routledge
ISBN: 9781351457637
Release Date: 2017-11-22
Genre: Mathematics

This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.

Measure Theory and Probability

Author: Malcolm Adams
Publisher: Springer Science & Business Media
ISBN: 9781461207795
Release Date: 2013-04-17
Genre: Mathematics

"...the text is user friendly to the topics it considers and should be very accessible...Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association