Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate students and researchers in all of these areas. Beginning with definitions of key concepts and fundamental results (Dilworth's and Sperner's theorem, interval and semiorders, Galois connection, duality with distributive lattices, coding and dimensi...

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s inco...

What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner.To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axio...

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophe...

This book contains revised and significantly extended versions of selected papers from three workshops on Uncertainty Reasoning for the Semantic Web (URSW), held at the International Semantic Web Conferences (ISWC) in 2011, 2012, and 2013. The 16 papers presented were carefully reviewed and selected from numerous submissions. The papers included in this volume are organized in topical sections on probabilistic and Dempster-Shafer models, fuzzy and possibilistic models, inductive reasoning ...

This book constitutes the refereed conference proceedings of the 22nd International Conference on Principles and Practice of Constraint Programming, CP 2016, held in Toulouse, France, in September 2016.The 63 revised regular papers presented together with 4 short papers and the abstracts of 4 invited talks were carefully reviewed and selected from 157 submissions. The scope of CP 2016 includes all aspects of computing with constraints, including theory, algorithms, environments, la...

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for fur...

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually ...

This book constitutes the refereed proceedings of the 22nd International Conference on Implementation and Application of Automata, CIAA 2017,held in Marne-la-Vallée, France, in June 2017.The 17 revised full papers presented were carefully reviewed and selected from 31 submissions. The topics of the presented papers include state complexity of automata; implementations of automata and experiments; enhanced regular expressions; and complexity analysis.

This book constitutes the refereed proceedings of the 16th Conference on Artificial Intelligence in Medicine, AIME 2017, held in Vienna, Austria, in June 2017.The 21 revised full and 23 short papers presented were carefully reviewed and selected from 113 submissions. The papers are organized in the following topical sections: ontologies and knowledge representation; Bayesian methods; temporal methods; natural language processing; health care processes; and machine learning, and a se...

This book constitutes the proceedings of the 13th International Symposium on Functional and Logic Programming, FLOPS 2016, held in Kochi, Japan, in March 2016.The 14 papers presented in this volume were carefully reviewed and selected from 36 submissions. They cover the following topics: functional and logic programming; program transformation and re-writing; and extracting programs from proofs of their correctness.

This book constitutes the refereed proceedings of the 11th International Haifa Verification Conference, HVC 2015, held in Haifa, Israel, in November 2015.The 17 revised full papers and 4 invited talks presented were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on hybrid systems; tools; verification of robotics; symbolic execution; model checking; timed systems; SAT solving; multi domain verification; and synthesis.