From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein's Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane's work in the early 1940's and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics.

From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein's Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane's work in the early 1940's and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics.

From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

This open access book constitutes the thoroughly refereed post-conference proceedings of the 6th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2020, held virtually in September 2020, associated with ECAI 2020, the 24th European Conference on Artificial Intelligence.The 7 revised full papers presented together with 2 invited contributions were reviewed and selected from 9 submissions. The contributions address various issues for knowledge representation and reasoning and the common graph-theoretic background, which allows to bridge the gap between the different communities.

This book constitutes the thoroughly refereed post-conference proceedings of the 5th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2017, held in Melbourne, VIC, Australia, in August 2017, associated with IJCAI 2017, the 26th International Joint Conference on Artificial Intelligence. The 7 revised full papers presented were reviewed and selected from 9 submissions. The contributions address various issues for knowledge representation and reasoning and the common graph-theoretic background allows to bridge the gap between the different communities.

This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2015, held in Buenos Aires, Argentina, in July 2015, associated with IJCAI 2015, the 24th International Joint Conference on Artificial Intelligence. The 9 revised full papers presented were carefully reviewed and selected from 10 submissions. The papers feature current research involved in the development and application of graph-based knowledge representation formalisms and reasoning techniques. They address the following topics: argumentation; conceptual graphs; RDF; and representations of constraint satisfaction problems.

The purpose of this book is to provide an overview of AI research, ranging from basic work to interfaces and applications, with as much emphasis on results as on current issues. It is aimed at an audience of master students and Ph.D. students, and can be of interest as well for researchers and engineers who want to know more about AI. The book is split into three volumes: - the first volume brings together twenty-three chapters dealing with the foundations of knowledge representation and the formalization of reasoning and learning (Volume 1. Knowledge representation, reasoning and learning) - the second volume offers a view of AI, in fourteen chapters, from the side of the algorithms (Volume 2. AI Algorithms) - the third volume, composed of sixteen chapters, describes the main interfaces and applications of AI (Volume 3. Interfaces and applications of AI). This second volume presents the main families of algorithms developed or used in AI to learn, to infer, to decide. Generic approaches to problem solving are presented: ordered heuristic search, as well as metaheuristics are considered. Algorithms for processing logic-based representations of various types (first-order formulae, propositional formulae, logic programs, etc.) and graphical models of various types (standard constraint networks, valued ones, Bayes nets, Markov random fields, etc.) are presented. The volume also focuses on algorithms which have been developed to simulate specific 'intelligent" processes such as planning, playing, learning, and extracting knowledge from data. Finally, an afterword draws a parallel between algorithmic problems in operation research and in AI.