Fundamentals of Logic and Computation

Although the fields of logic and computation are intrinsically related, most courses treat the two topics separately. This unique textbook aims to compress and unify important concepts of logical reasoning and computational theory, facilitating an in-depth understanding. Delivering theory with practical approaches, the book features early chapters accompanied by exercises in Isabelle/HOL, a popular and user-friendly theorem prover. Latter chapters address modelling and verification in Process Analysis Toolkit (PAT), a feature-rich model checker based on Hoare's Communicating Sequential Processes. The exposition focuses on the syntax, semantics and proof theory of various logics, as well as on automata theory, formal languages, computability, and complexity. It also builds a hybrid skill set of practical theorem proving and model checking, which will provide a solid grounding for future research or work involving formal methods.

Topicsand features:

• Offers a transition from logic to computation via linear temporal logic and state machines
• Includes exercises from widely-used software applications
• Provides entry-level tutorials for Isabelle/HOL and PAT
• Employs many examples from the Archives of Formal Proofs, as well as many examples of PAT models
• Introduces classical and nonclassical logics in an integrated presentation
• Discusses lambda calculus, recursive functions and Turing machines

• Concludes by addressing the Curry-Howard correspondence, which unifies logic and computationThe work is optimal for undergraduate students striving for a degree in computer science. In addition, it will be an excellent foundational volume for research students considering higher-degree research programs. Zhe Hou is a lecturer in the School of Information and Communication Technology at Griffith University, Nathan, Australia. His research pursuits include explainable AI, autonomous systems, formal verification, and automated reasoning.

Auteur

Zhe Hou is a lecturer in the School of Information and Communication Technology at Griffith University, Nathan, Australia. His research pursuits include explainable AI, autonomous systems, formal verification, and automated reasoning.

Texte du rabat

This textbook aims to help the reader develop an in-depth understanding of logical reasoning and gain knowledge of the theory of computation. The book combines theoretical teaching and practical exercises; the latter is realised in Isabelle/HOL, a modern theorem prover, and PAT, an industry-scale model checker. I also give entry-level tutorials on the two software to help the reader get started. By the end of the book, the reader should be proficient in both software. Content-wise, this book focuses on the syntax, semantics and proof theory of various logics; automata theory, formal languages, computability and complexity. The final chapter closes the gap with a discussion on the insight that links logic with computation. This book is written for a high-level undergraduate course or a Master's course. The hybrid skill set of practical theorem proving and model checking should be helpful for the future of readers should they pursue a research career or engineering in formal methods.

Contenu

1. Introduction to Logic.- 2. First-order Logic.- 3. Non-classical Logics.- 4. Automata Theory and Formal Languages.- 5. Turing Machines and Computability.- 6. Logic is Computation.