The 2nd Revised, Modified, and Enlarged Edition of Logics for Computer and Data Sciences, and Artificial Intelligence
Springer, 2023. — 489 p. — (Intelligent Systems Reference Library 245). — ISBN: 978-3-031-42033-7.
The book gives all interested in Computer Science, a deep review of relevant aspects of logic. In its scope are classical and non-classical logic. The content will be valid as well for those interested in linguistics, philosophy, and many other areas of research both in humane and technical branches of science as logic permeates all genuine realms of science. The book contains a substantial part of classical results in logic like those by Godel, Tarski, Church, and Rosser as well as later developments like many-valued logic, logics for knowledge engineering, first-order logics plus inductive definitions.
The exposition is rigorous yet without unnecessary abstractionism, so it should be accessible to readers from many disciplines of science. Each chapter contains a problem section, and problems are borrowed from research publications which allows for passing additional information, and allows readers to test their skills. An extensive bibliography of 270 positions directs readers to research works of importance.
This book concentrates on the presentation of the basic domains of logic which have great importance for the contemporary state of development of Computer Science (CS) and Artificial Intelligence (AI). This concerns, e.g., the application of logic as a very important tool for expressing concepts on which different forms of reasoning can be performed, deep characterization of the computational complexity of many different important problems in CS and AI as well as application of Boolean reasoning in different domains of CS and AI.
Moreover, the book also covers theoretical issues which yet have not been considered in the scope of CS or AI applications. Exploiting these issues more may lead to the discovery of new technologies. It is worthwhile mentioning that researchers in AI are gradually discovering the usefulness of advanced tools related to different branches of advanced mathematics and logic, e.g., topology and reasoning in solving the advanced problems related to Machine Learning. One can also observe that nowadays there is an important call to logicians, especially from AI, to develop new reasoning tools based on the relevant computing model necessary for solving challenges, related to, e.g., Intelligent Systems dealing with complex phenomena.
The material is presented in a very condensed and precise way. This concerns the whole book starting from the preliminary chapter which can serve as a basis for quite a few courses for graduate and Ph.D. students from CS and AI. It should be also noted that all theorems are presented together with detailed proofs.
Introduction: Prerequisites.
Sentential Logic (SL).
Rudiments of First-Order Logic (FO).
Modal and Intuitionistic Logics.
Temporal Logics for Linear and Branching Time and Model Checking.
Finitely and Infinitely Valued Logic.
Logics for Programs and Knowledge.
Beyond FO Within SO.