Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain. They are equipped with a formal logic-based semantics. Knowledge representation systems based on description logics provide various inference capabilities that deduce implicit knowledge from the explicitly represented knowledge. A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes.

Description Logics are a family of knowledge representation languages that have been studied extensively in Artificial Intelligence over the last two decades. They are embodied in several knowledge-based systems and are used to develop various real-life applications. The Description Logic Handbook provides a thorough account of the subject, covering all aspects of research in this field, namely: theory, implementation, and applications. Its appeal will be broad, ranging from more theoretically-oriented readers, to those with more practically-oriented interests who need a sound and modern understanding of knowledge representation systems based on Description Logics. The chapters are written by some of the most prominent researchers in the field, introducing the basic technical material before taking the reader to the current state of the subject, and including comprehensive guides to the literature. In sum, the book will serve as a unique reference for the subject, and can also be used for self-study or in conjunction with Knowledge Representation and Artificial Intelligence courses.

This book series consists of two parts, decidable description logics and undecidable description logics. It gives the R-calculi for description logics. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

This book introduces new models based on R-calculus and theories of belief revision for dealing with large and changing data. It extends R-calculus from first-order logic to propositional logic, description logics, modal logic and logic programming, and from minimal change semantics to subset minimal change, pseudo-subformula minimal change and deduction-based minimal change (the last two minimal changes are newly defined). And it proves soundness and completeness theorems with respect to the minimal changes in these logics. To make R-calculus computable, an approximate R-calculus is given which uses finite injury priority method in recursion theory. Moreover, two applications of R-calculus are given to default theory and semantic inheritance networks. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.

The Semantic Web is a worldwide endeavor to advance the Web by enriching its content with semantic metainformation that can be processed by inferen- enabled Web applications. Taxonomies and rules, along with their automated reasoning techniques, are the main components of Semantic Web ontologies. Rule systems are considered to be a major area in the further development of the Semantic Web. On one hand, rules can specify declarative knowledge in ontology languages, expressing constraints or transformations, either in conju- tionwith,orasanalternativeto,descriptionlogics.Ontheotherhand,rulescan specify behavioral knowledge, enforcing policies or reacting to events/changes. Finally, rule markup languages such as RuleML allow us to publish rules on the Web, to process rules in general XML environments as well as special rule engines, to exchange rules between di?erent applications and tools via XSLT translators, as well as to embed rules into other XML content and vice versa. This workshop was dedicated to all aspects of rules and rule markup l- guages for the Semantic Web. RuleML 2004 was the third in a series of wo- shops that was initiated with the International Semantic Web Conference. The previous workshops were held on Sardinia, Italy (2002), and on Sanibel Island, USA (2003). Thisyearwehad25submissions,ofwhich11wereacceptedasregularpapers and another ?ve as short papers describing tools. Wearegratefultoourtwoinvitedspeakers,MikeDeanfromBBNandChr- tine Golbreich from the University of Rennes. Our thanks also go to all subm- ters and reviewers without whom the workshop and these proceedings could not have succeeded.

This second volume of the book series shows R-calculus is a combination of one monotonic tableau proof system and one non-monotonic one. The R-calculus is a Gentzen-type deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. It discusses the algebraical and logical properties of tableau proof systems and R-calculi in many-valued logics. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.

Fuzzy systems and data mining are indispensible aspects of the computer systems and algorithms on which the world has come to depend. This book presents papers from FSDM 2021, the 7th International Conference on Fuzzy Systems and Data Mining. The conference, originally due to take place in Seoul, South Korea, was held online on 26-29 October 2021, due to ongoing restrictions connected with the COVID-19 pandemic. The annual FSDM conference provides a platform for knowledge exchange between international experts, researchers, academics and delegates from industry. This year, the committee received 266 submissions, and this book contains 52 papers, including keynotes and invited presentations, oral and poster contributions. The papers cover four main areas: 1) fuzzy theory, algorithms and systems – including topics like stability; 2) fuzzy applications – which are widely used and cover various types of processing as well as hardware and architecture for big data and time series; 3) the interdisciplinary field of fuzzy logic and data mining; and 4) data mining itself. The topic most frequently addressed this year is fuzzy systems. The book offers an overview of research and developments in fuzzy logic and data mining, and will be of interest to all those working in the field of data science.