The Automation of Proof PDF Download

Author: Donald A. MacKenzie
Publisher:
ISBN:
Category : Automatic theorem proving
Languages : en
Pages : 60

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Author: Melvin Fitting
Publisher: Springer Science & Business Media
ISBN: 1468403575
Category : Mathematics
Languages : en
Pages : 258

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Book Description
There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.

Author: Joseph E. Aoun
Publisher: MIT Press
ISBN: 0262549859
Category : Education
Languages : en
Pages : 221

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Book Description
A fresh look at a “robot-proof” education in the new age of generative AI. In 2017, Robot-Proof, the first edition, foresaw the advent of the AI economy and called for a new model of higher education designed to help human beings flourish alongside smart machines. That economy has arrived. Creative tasks that, seven years ago, seemed resistant to automation can now be performed with a simple prompt. As a result, we must now learn not only to be conversant with these technologies, but also to comprehend and deploy their outputs. In this revised and updated edition, Joseph Aoun rethinks the university’s mission for a world transformed by AI, advocating for the lifelong endeavor of a “robot-proof” education. Aoun puts forth a framework for a new curriculum, humanics, which integrates technological, data, and human literacies in an experiential setting, and he renews the call for universities to embrace lifelong learning through a social compact with government, employers, and learners themselves. Drawing on the latest developments and debates around generative AI, Robot-Proof is a blueprint for the university as a force for human reinvention in an era of technological change—an era in which we must constantly renegotiate the shifting boundaries between artificial intelligence and the capacities that remain uniquely human.

Author: Kevin Roose
Publisher: Hachette UK
ISBN: 152930475X
Category : Technology & Engineering
Languages : en
Pages : 256

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Book Description
A New York Times bestselling author and tech columnist's counter-intuitive guide to staying relevant - and employable - in the machine age by becoming irreplaceably human. It's not a future scenario any more. We've been taught that to compete with automation and AI, we'll have to become more like the machines themselves, building up technical skills like coding. But, there's simply no way to keep up. What if all the advice is wrong? And what do we need to do instead to become futureproof? We tend to think of automation as a blue-collar phenomenon that will affect truck drivers, factory workers, and other people with repetitive manual jobs. But it's much, much broader than that. Lawyers are being automated out of existence. Last year, JPMorgan Chase built a piece of software called COIN, which uses machine learning to review complicated contracts and documents. It used to take the firm's lawyers more than 300,000 hours every year to review all of those documents. Now, it takes a few seconds, and requires just one human to run the program. Doctors are being automated out of existence, too. Last summer, a Chinese tech company built a deep learning algorithm that diagnosed brain cancer and other diseases faster and more accurately than a team of 15 top Chinese doctors. Kevin Roose has spent the past few years studying the question of how people, communities, and organisations adapt to periods of change, from the Industrial Revolution to the present. And the insight that is sweeping through Silicon Valley as we speak -- that in an age dominated by machines, it's human skills that really matter - is one of the more profound and counter-intuitive ideas he's discovered. It's the antidote to the doom-and-gloom worries many people feel when they think about AI and automation. And it's something everyone needs to hear. In nine accessible, prescriptive chapters, Roose distills what he has learned about how we will survive the future, that the way to become futureproof is to become incredibly, irreplaceably human.

Author: Adam Chlipala
Publisher: MIT Press
ISBN: 0262317885
Category : Computers
Languages : en
Pages : 437

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Book Description
A handbook to the Coq software for writing and checking mathematical proofs, with a practical engineering focus. The technology of mechanized program verification can play a supporting role in many kinds of research projects in computer science, and related tools for formal proof-checking are seeing increasing adoption in mathematics and engineering. This book provides an introduction to the Coq software for writing and checking mathematical proofs. It takes a practical engineering focus throughout, emphasizing techniques that will help users to build, understand, and maintain large Coq developments and minimize the cost of code change over time. Two topics, rarely discussed elsewhere, are covered in detail: effective dependently typed programming (making productive use of a feature at the heart of the Coq system) and construction of domain-specific proof tactics. Almost every subject covered is also relevant to interactive computer theorem proving in general, not just program verification, demonstrated through examples of verified programs applied in many different sorts of formalizations. The book develops a unique automated proof style and applies it throughout; even experienced Coq users may benefit from reading about basic Coq concepts from this novel perspective. The book also offers a library of tactics, or programs that find proofs, designed for use with examples in the book. Readers will acquire the necessary skills to reimplement these tactics in other settings by the end of the book. All of the code appearing in the book is freely available online.

Author: Nachum Dershowitz
Publisher: Springer
ISBN: 9783540844884
Category : Computers
Languages : en
Pages : 564

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Book Description
This book constitutes the refereed proceedings of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2007, held in Yerevan, Armenia. It contains 36 revised full papers, 15 short papers and three invited talks that were carefully selected from 78 submissions. The papers address all current issues in logic programming, logic-based program manipulation, formal method, automated reasoning, and various kinds of AI logics.

Author: Hantao Zhang
Publisher: Springer Science & Business Media
ISBN: 9400916752
Category : Computers
Languages : en
Pages : 223

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Book Description
It has been shown how the common structure that defines a family of proofs can be expressed as a proof plan [5]. This common structure can be exploited in the search for particular proofs. A proof plan has two complementary components: a proof method and a proof tactic. By prescribing the structure of a proof at the level of primitive inferences, a tactic [11] provides the guarantee part of the proof. In contrast, a method provides a more declarative explanation of the proof by means of preconditions. Each method has associated effects. The execution of the effects simulates the application of the corresponding tactic. Theorem proving in the proof planning framework is a two-phase process: 1. Tactic construction is by a process of method composition: Given a goal, an applicable method is selected. The applicability of a method is determined by evaluating the method's preconditions. The method effects are then used to calculate subgoals. This process is applied recursively until no more subgoals remain. Because of the one-to-one correspondence between methods and tactics, the output from this process is a composite tactic tailored to the given goal. 2. Tactic execution generates a proof in the object-level logic. Note that no search is involved in the execution of the tactic. All the search is taken care of during the planning process. The real benefits of having separate planning and execution phases become appar ent when a proof attempt fails.

Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688

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Author: N. Shankar
Publisher: Cambridge University Press
ISBN: 9780521585330
Category : Computers
Languages : en
Pages : 224

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Book Description
Describes the use of computer programs to check several proofs in the foundations of mathematics.

Author: John Harrison
Publisher: Cambridge University Press
ISBN: 0521899575
Category : Computers
Languages : en
Pages : 703

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Book Description
A one-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.