Download or read book Software Abstractions written by Daniel Jackson and published by MIT Press. This book was released on 2012 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: An approach to software design that introduces a fully automated analysis giving designers immediate feedback, now featuring the latest version of the Alloy language. In Software Abstractions Daniel Jackson introduces an approach to software design that draws on traditional formal methods but exploits automated tools to find flaws as early as possible. This approach—which Jackson calls “lightweight formal methods” or “agile modeling”—takes from formal specification the idea of a precise and expressive notation based on a tiny core of simple and robust concepts but replaces conventional analysis based on theorem proving with a fully automated analysis that gives designers immediate feedback. Jackson has developed Alloy, a language that captures the essence of software abstractions simply and succinctly, using a minimal toolkit of mathematical notions. This revised edition updates the text, examples, and appendixes to be fully compatible with Alloy 4.

Download or read book The Art of Logic in an Illogical World written by Eugenia Cheng and published by Basic Books. This book was released on 2018-09-11 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.

Download or read book Levels Of Abstraction In Logic And Human Action written by Elliott Jaques and published by . This book was released on 1978-12-31 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Digital Logic Design written by Guy Even and published by Cambridge University Press. This book was released on 2012-10-08 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, based on the authors' fifteen years of teaching, is a complete teaching tool for turning students into logic designers in one semester. Each chapter describes new concepts, giving extensive applications and examples. Assuming no prior knowledge of discrete mathematics, the authors introduce all background in propositional logic, asymptotics, graphs, hardware and electronics. Important features of the presentation are: • All material is presented in full detail. Every designed circuit is formally specified and implemented, the correctness of the implementation is proved, and the cost and delay are analyzed • Algorithmic solutions are offered for logical simulation, computation of propagation delay and minimum clock period • Connections are drawn from the physical analog world to the digital abstraction • The language of graphs is used to describe formulas and circuits • Hundreds of figures, examples and exercises enhance understanding. The extensive website (http://www.eng.tau.ac.il/~guy/Even-Medina/) includes teaching slides, links to Logisim and a DLX assembly simulator.

Download or read book Abstract Algebraic Logic an Introductory Textbook written by Josep Maria Font and published by . This book was released on 2016-04-11 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract algebraic logic is the more general and abstract side of algebraic logic, the branch of mathematics that studies the connections between logics and their algebra-based semantics. This emerging subfield of mathematical logic consolidated since the 1980s, and is considered as the algebraic logic of the twenty-first century; as such it is increasingly becoming an indispensable tool to approach the algebraic study of any (mainly sentential) logic in a systematic way. This book is an introductory textbook on abstract algebraic logic, and takes a bottom-up approach, treating first logics with a simpler algebraic study, such as Rasiowa's implicative logics, and then guides readers, by means of successive steps of generalization and abstraction, to meet more and more complicated algebra-based semantics. An entire chapter is devoted to Blok and Pigozzi's theory of algebraizable logics, proving the main theorems and incorporating later developments by other scholars. After a chapter with the basics of the classical theory of matrices, one chapter is devoted to an in-depth exposition of the semantics of generalized matrices. There are also two more avanced chapters providing introductions to the two hierachies that organize the logical landscape according to the criteria of abstract algebraic logic, the Leibniz hierarchy and the Frege hierarchy. All throughout the book, particular care is devoted to the presentation and classification of dozens of examples of particular logics. The book is addressed to mathematicians and logicians with little or no previous exposure to algebraic logic. Some acquaintance with examples of non-classical logics is desirable in order to appreciate the extremely general theory. The book is written with students (or beginners in the field) in mind, and combines a textbook style in its main sections, including more than 400 carefully graded exercises, with a survey style in the exposition of some research directions. The book includes scattered historical notes and numerous bibliographic references.

Download or read book Everyday Abstract Conditional Reasoning written by András Veszelka and published by Pellea Humán Kutató és Fejlesztő Bt.. This book was released on 2014-07-04 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interpretation of the ‘if P then Q’ conditional statement is a central element in most logical systems. It largely shapes how these logical systems function. It is well known that, although attempts have been made, logical systems are principally unable to encapsulate how people reason in everyday life. This is mainly due to the discrepancies between the logical abstractions of the conditional statement and its everyday interpretation. Among other things, this makes it difficult to design artificial intelligence based on the abstract rules of logic. However, the ancient logicians who first defined the traditional interpretation of the conditional erroneously took into account more propositions than were actually being denoted. They characterised the ‘if P (or R) then Q’ relationship in place of the ‘if P then Q’ relationship. In relation to this, they also committed the error of leaving the context undenoted, which led to an unnatural interpretation of logical truth and logical necessity. This mistaken interpretation is still predominant today and can also be found in several mathematical logics, such as in propositional logic, even though mathematical logics were allegedly created independently of the ancient Greco-Roman logic. Fixing these problems reveals that the correct interpretation of the conditional statement is the equivalence/biconditional. This equivalent interpretation is interpreted by logicians as one of the most common everyday fallacies. Yet looking back on how the conditional statement was actually abstracted in the antiquity, it is evident that people were right and logicians were mistaken. Although the almost 50-year-old experimental psychological literature on the conditional did not confirm this common everyday tendency towards the biconditional interpretation, these findings are merely the result of unsystematic research. Running some of the long missing experiments leads the main experimental tasks to reveal overall the basic biconditional inferences. The approach presented in this book also resolves such dilemmas as the Wason’s abstract selection task, the paradox of the conditional statement and the Raven paradox. It is also shown here that the probabilistic interpretation of the conditional statement is not in conflict with this basic equivalent/biconditional interpretation. The approach is described in this book as the simplest possible non-monotonic logic, and pragmatic inferences, context effects, counterfactuals, possible world semantics and psychologism are also discussed. Since the conditional statement is equivalent to the universal affirmative statement in syllogisms, it is plausible to observe that fixing this same error in syllogisms also makes them compatible with people's actual inferences. Even the normally ambiguous Euler circles become an excellent tool to depict how this updated logic functions. Finally, with this new approach, the root of learning processes is inherently embedded into the logical abstraction of the conditional/universal affirmative statement, and hence, into logic in general. Therefore, this simple logic, presented in a non-technical way, has the potential to bring both human reasoning and learning under the umbrella of the same abstract system. This might be beneficial both for formalising psychology and for creating artificial intelligence.

Download or read book Levels of Abstraction in Logic and Human Action written by Elliott Jaques and published by Heinemann Educational Publishers. This book was released on 1978-01-01 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Logical Frameworks for Truth and Abstraction written by A. Cantini and published by Elsevier. This book was released on 1996-03-14 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential. These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these theories provide a new outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications. Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered. Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field.

Download or read book Software Abstractions revised edition written by Daniel Jackson and published by MIT Press. This book was released on 2016-02-12 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: An approach to software design that introduces a fully automated analysis giving designers immediate feedback, now featuring the latest version of the Alloy language. In Software Abstractions Daniel Jackson introduces an approach to software design that draws on traditional formal methods but exploits automated tools to find flaws as early as possible. This approach—which Jackson calls “lightweight formal methods” or “agile modeling”—takes from formal specification the idea of a precise and expressive notation based on a tiny core of simple and robust concepts but replaces conventional analysis based on theorem proving with a fully automated analysis that gives designers immediate feedback. Jackson has developed Alloy, a language that captures the essence of software abstractions simply and succinctly, using a minimal toolkit of mathematical notions. This revised edition updates the text, examples, and appendixes to be fully compatible with Alloy 4.

Download or read book The Limits of Abstraction written by Kit Fine and published by Clarendon Press. This book was released on 2002 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Limits of Abstraction breaks new ground both technically and philosophically, and is essential reading for all those working on the philosophy of mathematics."--BOOK JACKET.

Download or read book An Introduction to Modern Logic written by Rupert Clendon Lodge and published by . This book was released on 1920 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sets Functions and Logic written by Keith Devlin and published by CRC Press. This book was released on 2018-10-03 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students. Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead. Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read...and enjoy...and learn from. About the Author Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,. Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.

Download or read book Abstraction Refinement and Proof for Probabilistic Systems written by Annabelle McIver and published by Springer Science & Business Media. This book was released on 2005 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an integrated coverage of random/probabilistic algorithms, assertion-based program reasoning, and refinement programming models, providing a focused survey on probabilistic program semantics. This book illustrates, by examples, the typical steps necessary to build a mathematical model of any programming paradigm.

Download or read book Logical Form written by Andrea Iacona and published by Springer. This book was released on 2018-01-28 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfill two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language.

Download or read book Science and an African Logic written by Helen Verran and published by University of Chicago Press. This book was released on 2001-12-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Does two and two equal four? Ask someone and they should answer yes. An equation such as this seems the very definition of certainty, but is it? In this book, Helen Verran addresses precisely that question.

Download or read book Logic Abstraction written by Edith Altamiranda and published by . This book was released on 2005 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Abstraction and Infinity written by Paolo Mancosu and published by Oxford University Press. This book was released on 2016 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mancosu offers an original investigation of key notions in mathematics: abstraction and infinity, and their interaction. He gives a historical analysis of the theorizing of definitions by abstraction, and explores a novel approach to measuring the size of infinite sets, showing how this leads to deep mathematical and philosophical problems.