Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in ph...

This book constitutes the proceedings of the 12th International Symposium on Frontiers of Combining Systems, FroCoS 2019, held in London, UK, in September 2019, colocated with the 28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2019.The 20 papers presented were carefully reviewed and selected from 30 submissions. They present research on the development of techniques and methods for the combination and integration of formal ...

This book constitutes the refereed proceedings of the 5th International Conference on Logic and Argumentation, CLAR 2023, held in Hangzhou, China, during September 10-12, 2023.The 11 full papers, one short paper and one invited paper presented in this book were carefully reviewed and selected from 20 submissions.The papers focus on topics such as:logic and automated deduction; abstract and structured argumentation; dialogues, games and practical reasoning; and quantitative ...

This LNCS book is part of the FOLLI book series and constitutes the proceedings of the 9th International Workshop on Logic, Rationality, and Interaction, LORI 2023, held in Jinan, China, in October 2023.The 15 full papers presented together with 7 short papers in this book were carefully reviewed and selected from 40 submissions. The workshop covers a wide range on the following topics such as agency; argumentation and agreement; beliefrepresentation; probability and uncert...

Despite growing interest, basic information on methods and models for mathematically analyzing algorithms has rarely been directly accessible to practitioners, researchers, or students. An Introduction to the Analysis of Algorithms, Second Edition, organizes and presents that knowledge, fully introducing primary techniques and results in the field.Robert Sedgewick and the late Philippe Flajolet have drawn from both classical mathematics and computer scienc...

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a bro...

Machine learning is one of the fastest growing areas of computer science, with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way. The book provides a theoretical account of the fundamentals underlying machine learning and the mathematical derivations that transform these principles into practical algorithms. Following a presentation of the basics, the book covers a wide array of central topics ...

Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning whi...

The conclusion reached in "Fathoming Gödel" is that Gödel's 1931 paper is a shell game. It is based on several errors that are well camouflaged. Some shortcomings in the paper are openly admitted although they are downplayed, and errors are also produced in an effort to force a particular conclusion. This critique is limited to Gödel's first incompleteness theorem as translated by Martin Hirzel. "Fathoming Gödel" is an examination of Kurt Gödel's 1931 paper: "On formally undecidable propos...

Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science.The common approach to presenting ...

Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of...

The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive...