The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob­ lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom­ pleteness".

Machine learning and cybernetics play an important role in many modern electronic, computer and communications systems. Automated processing of information by these systems requires intelligent analysis of various types of data and optimal decision making. In recent years, we have witnessed a rapid expansion of research and development activities in machine learning and cybernetics. To provide opportunities for researchers in these areas to share their ideas and foster collaborations, the International Conference on Machines and Cybernetics (ICMLC) has been held annually since 2002. The conference series has achieved a great success in attracting a large number of paper submissions and participants and enabling fruitful exchanges among academic and industrial researchers and postgraduate students. In 2005, the conference (ICMLC 2005) received 2461 full paper submissions and the Program Committee selected 1050 of them for presentation. It is especially encouraging that the conference is attracting more and more international attention. This year, there are contributions from 21 countries and 211 universities worldwide. Out of the 1050 papers presented at the conference, we selected 114 papers to be published in this volume of Lecture Notes in Computer Science.

This book is dedicated to the life and work of logician Janusz Czelakowski on the topic of logical consequence. It consists of three parts – a biography, a survey and research sections. The volume begins with an autobiographic chapter by Janusz Czelakowski followed by a historical chapter written by Jacek Malinowski.

Winner of the 1983 National Book Award, The Mathematical Experience presented a highly insightful overview of mathematics that effectively conveyed its power and beauty to a large audience of mathematicians and non-mathematicians alike. The study edition of the work followed about a decade later, supplementing the original material of the book with exercises to provide a self-contained treatment usable for the classroom.

Formal methods are a robust approach for problem solving. It is based on logic and algebraic methods where problems can be formulated in a way that can help to find an appropriate solution. This book shows the basic concepts of formal methods and highlights modern modifications and enhancements to provide a more robust and efficient problem solving tool.

Adaptive Resonance Theory Microchips describes circuit strategies resulting in efficient and functional adaptive resonance theory (ART) hardware systems. While ART algorithms have been developed in software by their creators, this is the first book that addresses efficient VLSI design of ART systems. All systems described in the book have been designed and fabricated (or are nearing completion) as VLSI microchips in anticipation of the impending proliferation of ART applications to autonomous intelligent systems. To accommodate these systems, the book not only provides circuit design techniques, but also validates them through experimental measurements. The book also includes a chapter tutorially describing four ART architectures (ART1, ARTMAP, Fuzzy-ART and Fuzzy-ARTMAP) while providing easily understandable MATLAB code examples to implement these four algorithms in software. In addition, an entire chapter is devoted to other potential applications for real-time data clustering and category learning.

Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems.

Algorithmic design, especially for hard problems, is more essential for success in solving them than any standard improvement of current computer tech­ nologies. Because of this, the design of algorithms for solving hard problems is the core of current algorithmic research from the theoretical point of view as well as from the practical point of view. There are many general text books on algorithmics, and several specialized books devoted to particular approaches such as local search, randomization, approximation algorithms, or heuristics.

The Idea of Program Refinement Programs are complex. They are typically so complex, that they go beyond the full comprehension even of the programmer or team who designed them, with all the consequences this has. How can we cope with such complexity in a satisfactory way? An approach, advocated for a long time, is to separate a concise specification of a program - the "what" - from a possibly involved implementation - the "how". Once a specification is obtained from the set of requirements on the program, there can still be a large gap to an efficient implementation. The development from specification to implementation can then proceed by a succession oflayers, such that each layer is a refinement of the previous one. Design decisions can be introduced in refinement steps one at a time. By this, the refinement steps can be kept small and manageable.

Petri nets do not designate a single modeling formalism. In fact, newcomers to the field confess sometimes to be a little puzzled by the diversity of formalisms that are recognized under this "umbrella". Disregarding some extensions to the theoretical modeling capabilities, and looking at the level of abstraction of the formalisms, Condition/Event, Elementary, Place/Transition, Predicate/Transition, Colored, Object Oriented… net systems are frequently encountered in the literature. On the other side, provided with appropriate interpretative extensions, Controled Net Systems, Marking Diagrams (the Petri net generalization of State Diagrams), or the many-many variants in which time can be explicitly incorporated -Time(d), Deterministic, (Generalized) Stochastic, Fuzzy…- are defined. This represents another way to define practical formalisms that can be obtained by the "cro- product" of the two mentioned dimensions. Thus Petri nets constitute a modeling paradigm, understandable in a broad sense as "the total pattern of perceiving, conceptualising, acting, validating and valuing associated with a particular image of reality that prevails in a science or a branch of science" (Thomas S. Kuhn).

This book constitutes the refereed proceedings of the 32nd International Conference on Inductive Logic Programming, ILP 2023, held in Bari, Italy, during November 13–15, 2023. The 11 full papers and 1 short paper included in this book were carefully reviewed and selected from 18 submissions. They cover all aspects of learning in logic, multi-relational data mining, statistical relational learning, graph and tree mining, learning in other (non-propositional) logic-based knowledge representation frameworks, exploring intersections to statistical learning and other probabilistic approaches.

There's so much talk about the threat posed by intelligent machines that it sometimes seems as though we should surrender to our robot overlords now. But Junaid Mubeen isn't ready to throw in the towel just yet.

From the viewpoint of an "industrial" this book is most welcome, as one of the most significant demonstrations of the maturity of Prolog. Logic programming is a fascinating area in computer science, which held for years - and still does - the promise of freeing ourselves from programming based on the "Von Neumann" machine. In addition computer programming has long been for solid theoretical foundations. While conventional engineering, dealing mainly with "analogical complexity", developed over some hundred years a complete body of mathematical tools, no such toolset was available for "digital complexity". The only mathematical discipline which deals with digital complexity is logic and Prolog is certainly the operational tool which comes closest to the logical programming ideal. So, why does Prolog, despite nearly twenty years of development, still appear to many today to be more of a research or academic tool, rather than an industrial programming language? A few reasons may explain this: First, I think Prolog suffers from having been largely assimilated into - and thus followed the fate of - Artificial Intelligence. Much hype in the late 1980 created overexpectations and failed to deliver, and the counterreaction threw both AI and Prolog into relative obscurity. In a way, maybe this is a new chance for the Prolog community: the ability to carry out real work and progress without the disturbance of limelights and the unrealistic claims of various gurus. Second, programming in Prolog is a new experience for computer professionals.

Precisely 50 years ago the first volume of Studia Logica appeared. The present volume celebrates the 50th Anniversay of Studia Logica - An Inter- national Joumal for Symbolic Logic. The papers in this Anniversary volume are the results of the two conferences Trends in Logic - 50 Years of Studia Logica.