This comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory updates the author's work over the past 12 years, and describes the latest general ideas and open ...problems in this expanding field.
This paper briefly discusses the relations between logic and metalogic in history. Metalogic is understood as a reflection on logic in its various senses, particularly
(formal, mathematical) and
...(formal logic plus semantic plus methodology of science). It is shown that metalogic in its contemporary understanding arose after mathematical logic had become a mature discipline. Special passage is devoted to metalogic in Poland. The last part of the paper discussed so-called logocentric predicament.
The article presents and justifies the thesis that the way of understanding knowledge has changed significantly over the last century. This change consists in departing from the classic definition of ...knowledge formulated by Plato, and in particular in questioning the subjective role of man as the holder of knowledge and abandoning claims to the truthfulness of knowledge. This process was an intensive evolution; its elements are given and justified in the text. Its source was a deep reconstruction of the mode of creating epistemic structures in mathematics and geometry, based on the abandonment of the principle of representation. Knowledge turned out to be determined by the social context, it became dispersed, decentralized, which led to the rejection of the condition of its truthfulness. The last phase of this evolution is knowledge as a phenomenon in the area of digital technologies, in particular artificial intelligence. This evolution has led to the emergence of many variants of knowledge that act as local knowledge, which justifies the use of the plural in this case.
This volume is a systematic, expansive presentation of the major achievements in the intersection between two fields of inquiry: Argumentation Theory and Artificial Intelligence. Contributions from ...international researchers who have helped shape this dynamic area offer a progressive development of intuitions, ideas and techniques, from philosophical backgrounds, to abstract argument systems, to computing arguments, to the appearance of applications producing innovative results. Each chapter features extensive examples to ensure that readers develop the right intuitions before they move from one topic to another. In particular, the book exhibits an overview of key concepts in Argumentation Theory and of formal models of Argumentation in AI. After laying a strong foundation by covering the fundamentals of argumentation and formal argument modeling, the book expands its focus to more specialized topics, such as algorithmic issues, argumentation in multi-agent systems, and strategic aspects of argumentation. Finally, as a coda, the book explores some practical applications of argumentation in AI and applications of AI in argumentation. Argumentation in Artificial Intelligence is sure to become an essential resource for graduate students and researchers working in Autonomous Agents, AI and Law, Logic in Computer Science, Electronic Governance, and Multi-agent Systems. The book is suitable both as a comprehensive introduction to the field, and also as a highly organized and accessible reference for established researchers.
Analysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called ...the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology - fixed points, cycles, transient times and basins of attractors - can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling etc.
This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It ...provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.
Hybrid systems describe the interaction of software, modeled by finite-state systems such as finite-state machines, with the physical world, described by infinite-state systems such as differential ...equations. Verification and Control of Hybrid Systems provides a unique systematic exposition of several classes of hybrid systems, admitting symbolic models along with the relationships between them. The text outlines several key verification and control synthesis results for hybrid systems, guided by the concept of bisimulation, and illustrated by numerous examples. The book is divided into four parts: Part I presents basic concepts centered on a notion of system that is general enough to describe finite-state, infinite-state, and hybrid systems. Part II discusses the ways in which systems relate to other systems, such as behavioral inclusion/equivalence and simulation/bisimulation, using these relationships to study verification and control synthesis problems for finite-state systems. Part III draws inspiration from timed automata to present several classes of hybrid systems, with richer continuous dynamics, that can be related to finite-state symbolic systems. Once such relationships are established, verification and control synthesis problems for these hybrid systems can be immediately solved by resorting to the techniques described in Part II for finite-state systems. Part IV follows the same strategy by generalizing simulation/bisimulation relationships to approximate simulation/bisimulation relationships that can be used for a wider class of hybrid systems. This comprehensive treatment will appeal to researchers, engineers, computer scientists, and graduate students in the areas of formal methods, verification, model checking, and control and will undoubtedly inspire further study of the specialized literature.
I have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel… I found it hard to stop reading before I finished (in two days) the whole text. ...Soifer engages the readers attention not only mathematically, but emotionally and esthetically. May you enjoy the book as much as I did! – Branko Grünbaum University of Washington You are doing great service to the community by taking care of the past, so the things are better understood in the future. –Stanislaw P. Radziszowski, Rochester Institute of Technology They Van der Waerden’s sections meet the highest standards of historical scholarship. – Charles C. Gillispie, Princeton University You have dug up a great deal of information – my compliments! – Dirk van Dalen, Utrecht University I have just finished reading your (second) article in search of van der Waerden. It is a masterpiece, I could not stop reading it... Congratulations! – Janos Pach, Courant Institute of Mathematics Mathematical Coloring Book will (we can hope) have a great and salutary influence on all writing on mathematics in the future.““ - Peter D. Johnson Jr., Auburn University
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