Published in honor of Daniele Mundici on the occasion of his 60th birthday, the 17 revised papers of this Festschrift volume include invited extended versions of the most interesting contributions to the International Conference on the Algebraic and Logical Foundations of Many-Valued Reasoning, held in Gargnano, Italy, in March 2006. Edited in collaboration with FoLLI, the Association of Logic, Language and Information, it is the third volume of the FoLLI LNAI subline.

This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.

This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic.

This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.

Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).

The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XXII in the series is a continuation of a number of research streams that have grown out of the seminal work of Zdzislaw Pawlak during the first decade of the 21st century.

Belief Revision Refutation and systems in Propositional Logic. A Quantifier Scope in Formal Linguistics and Non-deterministic Semantics for Logical Systems.

The scientific area this thesis belongs to is many-valued logics: this meanslogics in which, from the semantical point of view, we have "intermediate"truth-values, between 0 and 1 (which in turns are designated to represent, respectively, the "false" and the "true").The classical logic (propositional, for simplicity) is based on the fact thatevery statement is true or false: this is reflected by the excluded middle law, that is a theorem of this logic. However, there are many reasons that suggestto reject this law: for example, intuitionistic logic does not satisfy it, sincethis logic reflects a "constructive" conception of mathematics (see [Hey71, Tro69]).

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 25th Workshop on Logic, Language, Information and Communication, WoLLIC 2018, held inBogota, Colombia, in July 2018. The 16 full papers together with 3 short papers and 3 invited talks presented were fully reviewed and selected from 30 submissions. The vision for the conference is to provide an annual forum which is large enough to provide meaningful interactions between logic and the sciences related to information and computation.

This book is composed of selected papers presented at IWIFSGN'2019—The Eighteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets—held on October 24–25, 2019, in Warsaw, Poland, which is one of the main conferences on fuzzy logic, notably on extensions of the traditional fuzzy sets, in particular on the intuitionistic fuzzy sets. A considerable part of the conference sessions is also concerned with recent developments and challenges in the theory and applications of other topics exemplified by uncertainty, incompleteness and imprecision modeling, the Generalized Nets (GNs), a powerful extension of the traditional Petri net paradigm, and the InterCriteria Analysis, a new method for the feature selection and analyses in multicriteria and multiattribute decision-making problems. Some more general problems of computational and artificial intelligence, exemplified by evolutionary computations, machine learning, etc., are also dealt with. The papers included yield a good perspective on all of these important issues and problems.