This textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained. Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation. Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus. After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications. The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics. Sequents and Trees is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics. It will also be of interest to researchers in computer science and philosophers.

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 presents the papers delivered at the Conference on Systems and Computer Science held at the University of Western Ontario in September 1965. The primary purposes of the Conference were the promotion of research and the development of the teaching of computer science in Canadian universities. The papers focus attention on some of the concepts of Computer Science as a new field of study and at the same time provide a background for scientists looking at the subject for the first time. The chief developments in computer science have been concerned with the "applied" rather than the "pure" areas of the field: numerical analysis, applied statistics and operations research, and data processing. But there is something more to computers than the physical components and this book represents an attempt to correct the imbalance between "applied" and "pure" by drawing attention to certain theoretical aspects of computer and information science. Among the topics discussed are the theory of finite and infinite automata, aspects of formal language theory, heuristic and non-heuristic approaches to theorem proving and the mathematical formulation of the theory of general systems. There are also references to the problems of machine design, to software systems including higher-level languages, to multiple control computer models and to applied systems. This collection of papers will appeal first to graduate students and professors in Computer Science. It will also be of interest to computer scientists in industry and in government and university research groups and to the scientific public interested in discovering some of the principal ingredients and directions of the computer and information sciences.

This book constitutes the refereed proceedings of the 5th Asian Computing Science Conference, ASIAN'99, held in Phuket, Thailand, in December 1999. The 28 revised full papers presented together with two invited contributions and 11 short presentations were carefully reviewed and selected from a total of 114 submissions. Among the topics addressed are programming theory, formal methods, automated reasoning, verification, embedded systems, real-time systems, distributed systems, and mobile computing.

An introduction to natural language semantics that offers an overview of the empirical domain and an explanation of the mathematical concepts that underpin the discipline. This textbook offers a comprehensive introduction to the fundamentals of those approaches to natural language semantics that use the insights of logic. Many other texts on the subject focus on presenting a particular theory of natural language semantics. This text instead offers an overview of the empirical domain (drawn largely from standard descriptive grammars of English) as well as the mathematical tools that are applied to it. Readers are shown where the concepts of logic apply, where they fail to apply, and where they might apply, if suitably adjusted. The presentation of logic is completely self-contained, with concepts of logic used in the book presented in all the necessary detail. This includes propositional logic, first order predicate logic, generalized quantifier theory, and the Lambek and Lambda calculi. The chapters on logic are paired with chapters on English grammar. For example, the chapter on propositional logic is paired with a chapter on the grammar of coordination and subordination of English clauses; the chapter on predicate logic is paired with a chapter on the grammar of simple, independent English clauses; and so on. The book includes more than five hundred exercises, not only for the mathematical concepts introduced, but also for their application to the analysis of natural language. The latter exercises include some aimed at helping the reader to understand how to formulate and test hypotheses.

This book constitutes the refereed conference proceedings of the 28th International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, IEA/AIE 2015, held in Seoul, South Korea, in June 2015. The 73 revised full papers presented were carefully reviewed and selected from 105 submissions. The papers cover a wide range of topics in applied artificial intelligence including reasoning, robotics, cognitive modeling, machine learning, pattern recognition, optimization, text mining, social network analysis, and evolutionary algorithms. They are organized in the following topical sections: theoretical AI, knowledge-based systems, optimization, Web and social networks, machine learning, classification, unsupervised learning, vision, image and text processing, and intelligent systems applications.

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.