The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers.
Das Unendliche hat wie keine andere Frage von jeher so tief das Gemüt der Menschen bewegt," das Unendliche hat wie kaum eine andere Idee auf den Verstand so an regend und fruchtbar gewirkt," das Unendliche ist aber auch wie kein anderer Begriff so der Aufklärung bedürftig.
The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s.
Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information.
The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, sociology, physics.
This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice.
Knowledge of automata theory and formal languages is crucial for understanding human-computer interaction, as well as for understanding the various processes that take place when manipulating knowledge if that knowledge is, indeed, expressed as sentences written in a suitably formalized language.
This book provides a hands-on introduction to runtime verification which guides the reader from zero to sufficient practical knowledge required to consider and apply it in industry.
This book defines a logical system called the Protocol-theoretic Logic of Epistemic Norms (PLEN), it develops PLEN into a formal framework for representing and reasoning about epistemic norms, and it shows that PLEN is theoretically interesting and useful with regard to the aims of such a framework.
This volume offers English translations of three early works by Ernst Schroder (1841-1902), a mathematician and logician whose philosophical ruminations and pathbreaking contributions to algebraic logic attracted the admiration and ire of figures such as Dedekind, Frege, Husserl, and C.
This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact.
This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation.
This volume contains English translations of Godel's chapters on logicism and the antinomies and on the calculi of pure logic, as well as outlines for a chapter on metamathematics.
A significant number of works have set forth, over the past decades, the emphasis laid by seventeenth-century mathematicians and philosophers on motion and kinematic notions in geometry.
The purpose of the Reasoning Web Summer School is to disseminate recent advances on reasoning techniques and related issues that are of particular interest to Semantic Web and Linked Data applications.
This book constitutes the proceedings of the 23rd International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2022, which took place in Philadelphia, PA, USA, in January 2022.
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2022, held in Deerfield Beach, FL, USA, in January 2022.
This book focuses on one of the major challenges of the newly created scientific domain known as data science: turning data into actionable knowledge in order to exploit increasing data volumes and deal with their inherent complexity.
The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century.
This book constitutes the refereed proceedings of the 4th International Workshop and Tutorial, FMTea 2021, Held as Part of the 4th World Congress on Formal Methods, FM 2021, as a virtual event in November 2021.
This book constitutes the proceedings of the 19th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2021, which took place in Marseille, France, during November 2-5, 2021.
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia.
This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas.
This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications.
This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics.
This book centers around a dialogue between Roger Penrose and Emanuele Severino about one of most intriguing topics of our times, the comparison of artificial intelligence and natural intelligence, as well as its extension to the notions of human and machine consciousness.
This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures.
This textbook covers key topics of Elementary Calculus through selected exercises, in a sequence that facilitates development of problem-solving abilities and techniques.
This survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing.
This book describes some basic principles that allow developers of computer programs (computer scientists, software engineers, programmers) to clearly think about the artifacts they deal with in their daily work: data types, programming languages, programs written in these languages that compute from given inputs wanted outputs, and programs that describe continuously executing systems.
