Автор: Hantao Zhang, Jian Zhang
Издательство: Springer
Год: 2025
Страниц: 488
Язык: английский
Формат: pdf (true), epub
Размер: 28.8 MB
Mathematical logic is an important basis for mathematics, Computer Science and Artificial Intelligence (AI) alike. This book provides a comprehensive introduction to various logics, including classical propositional logic and first-order predicate logic, as well as equational logic, temporal logic, and Hoare logic. In addition, it presents proof procedures for classical logics and decision procedures for checking the satisfiability of logical formulas.
The book assumes no background in logic. It presents logics as practical tools for solving various problems in Artificial Intelligence and formal verification. Accordingly, it is well suited for (junior and senior) undergraduate and graduate students majoring in Computer Science or mathematics. Each chapter has about a dozen or so exercises to help the reader understand the materials.
The focus of the book is to present algorithms in the form of proof procedures for the classical logics and decision procedures for checking the satisfiability of logical formulas. A large portion of the book is devoted to the introduction of software tools based on these algorithms and the practical problems which can be solved by these tools in constraint satisfaction, formal verification, and Artificial Intelligence.
Logic has been called the calculus of Computer Science, because logic is fundamental in Computer Science, similar to calculus in the physical and engineering sciences. Logic is used in almost every field of Computer Science: computer architecture (such as digital gates, hardware verification), software engineering (specification and verification), programming languages (semantics, type theory, abstract data types, object-oriented programming), databases (relational algebra), Artificial Intelligence (automated theorem proving, knowledge representation), algorithms and theory of computation (complexity, computability), etc.
- Provides a comprehensive introduction to various logics related to Computer Science;
- Presents key algorithms for automated reasoning, including some new algorithms;
- Introduces state-of-the-art logic tools, including SAT and SMT solvers and resolution-based provers
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