Author: Mauricio Ayala-Rincón Publisher: Springer ISBN: 3319516531 Category : Computers Languages : en Pages : 165
Book Description
This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available in modern proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians and engineers to increment their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems. The authors present a concise overview of the necessary computational and mathematical aspects of ‘logic’, placing emphasis on both natural deduction and sequent calculus. Differences between constructive and classical logic are highlighted through several examples and exercises. Without neglecting classical aspects of computational logic, the authors also highlight the connections between logical deduction rules and proof commands in proof assistants, presenting simple examples of formalizations of the correctness of algebraic functions and algorithms in PVS. Applied Logic for Computer Scientists will not only benefit students of computer science and mathematics but also software, hardware, automation, electrical and mechatronic engineers who are interested in the application of formal methods and the related computational tools to provide mathematical certificates of the quality and accuracy of their products and technologies.
Author: László Pólos Publisher: Springer Science & Business Media ISBN: 9401585334 Category : Philosophy Languages : en Pages : 394
Book Description
A selection of papers presented at the international conference `Applied Logic: Logic at Work', held in Amsterdam in December 1992. Nowadays, the term `applied logic' has a very wide meaning, as numerous applications of logical methods in computer science, formal linguistics and other fields testify. Such applications are by no means restricted to the use of known logical techniques: at its best, applied logic involves a back-and-forth dialogue between logical theory and the problem domain. The papers focus on the application of logic to the study of natural language, in syntax, semantics and pragmatics, and the effect of these studies on the development of logic. In the last decade, the dynamic nature of natural language has been the most interesting challenge for logicians. Dynamic semantics is here applied to new topics, the dynamic approach is extended to syntax, and several methodological issues in dynamic semantics are systematically investigated. Other methodological issues in the formal studies of natural language are discussed, such as the need for types, modal operators and other logical operators in the formal framework. Further articles address the scope of these methodological issues from other perspectives ranging from cognition to computation. The volume presents papers that are interesting for graduate students and researchers in the field of logic, philosophy of language, formal semantics and pragmatics, and computational linguistics.
Author: Pei Wang Publisher: Springer Science & Business Media ISBN: 1402050453 Category : Computers Languages : en Pages : 420
Book Description
This book is the most comprehensive description of the decades-long Non-Axiomatic Reasoning System (NARS) project, including its philosophical foundation, methodological consideration, conceptual design details, implications in the related fields, and its similarities and differences to many related works in cognitive science. While most current works in Artificial Intelligence (AI) focus on individual aspects of intelligence and cognition, NARS is designed and developed to attack the AI problem as a whole.
Author: László Pólos Publisher: Springer Science & Business Media ISBN: 9780792334323 Category : Computers Languages : en Pages : 408
Book Description
Other methodological issues in the formal studies of natural language are discussed, such as the need for types, modal operators and other logical operators in the formal framework. Further articles address the scope of these methodological issues from other perspectives ranging from cognition to computation.
Author: Walter Carnielli Publisher: Springer Science & Business Media ISBN: 1402067828 Category : Mathematics Languages : en Pages : 612
Book Description
Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.
Author: Michael Masuch Publisher: Springer Science & Business Media ISBN: 9783540580959 Category : Computers Languages : en Pages : 252
Book Description
This volume is based on the International Conference Logic at Work, held in Amsterdam, The Netherlands, in December 1992. The 14 papers in this volume are selected from 86 submissions and 8 invited contributions and are all devoted to knowledge representation and reasoning under uncertainty, which are core issues of formal artificial intelligence. Nowadays, logic is not any longer mainly associated to mathematical and philosophical problems. The term applied logic has a far wider meaning, as numerous applications of logical methods, particularly in computer science, artificial intelligence, or formal linguistics, testify. As demonstrated also in this volume, a variety of non-standard logics gained increased importance for knowledge representation and reasoning under uncertainty.
Author: Wei Li Publisher: Springer Science & Business Media ISBN: 3764399775 Category : Mathematics Languages : en Pages : 273
Book Description
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.
Author: Ulrich Kohlenbach Publisher: Springer Science & Business Media ISBN: 3540775331 Category : Mathematics Languages : en Pages : 539
Book Description
This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as – via extended case studies – carrying out some of these applications in full detail. This subject has historical roots in the 1950s. This book for the first time tells the whole story.
Author: Aldo Ursini Publisher: Routledge ISBN: 1351434721 Category : Mathematics Languages : en Pages : 728
Book Description
""Attempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s.
Author: Peter B. Andrews Publisher: Springer Science & Business Media ISBN: 9781402007637 Category : Computers Languages : en Pages : 416
Book Description
In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
Author: Mauricio Ayala-Rincón
Author: László Pólos
Author: Pei Wang
Author: László Pólos
Author: Walter Carnielli
Author: Michael Masuch
Author: Wei Li
Author: Ulrich Kohlenbach
Author: Aldo Ursini
Author: Peter B. Andrews