الصفحة 1
الصفحة 1
New Computational Paradigms : Changing Conceptions of What is Computable
This book examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. The book opens with an introduction by Andrew Hodges, the Turing biographer, who analyzes the pioneering work that anticipated recent developments concerning computation’s allegedly new paradigms. The remaining material covers traditional topics in computability theory such as relative computability, theory of numberings, and domain theory, in addition to topics on the relationships between proof theory, computability, and complexity theory.
Information and knowledge : A constructive type-theoretical approach
This book develops a philosophical and logical interpretation of the concept of information within the formal structure of Constructive Type Theory (CTT), in a manner concurrent with a diverse range of contemporary perspectives on the philosophy of information. On the basis of this conceptual framework, the problem of analyticity for logical derivations is faced and a solution is proposed.The text begins with a presentation of the formal structure of CTT, paying particular attention to some topics that have been neglected by current researchers in Type Theory. Information and Knowledge presents a new interesting perspective on the constructive interpretation of knowledge processes, suggesting the reliability of such an approach for the logical modeling of epistemic problems and proposing a unifying frame from one of the more important contemporary philosophical perspectives.
Guida alla teoria degli insiemi = Guide to set theory
Teachers are in difficulty with regard to the space and emphasis to be given to set theory topics, in their preparation and in their work, because they have not been provided with adequate knowledge at the university. It is safe to say, on the basis of much experience, that the average mathematician, even the researcher, does not know what set theory is. Two prejudices stand in the way of a good knowledge of the theory: one, of a minimalist type, is its identification with an unspecified "set theory", an austere language that is too demanding if one wants to impose it prematurely; the other is of a maximalist type and consists in the supposed and effective link with the more subtle questions of the foundations of mathematics. But the theory has an important mathematical content, and with many implications of didactic interest.
Foundations of software science and computation structures ; 25th International conference, FOSSACS 2022, Held as Part of the European joint conferences on theory and practice of software, ETAPS 2022, Munich, Germany, April 2–7, 2022, proceedings
This book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.
Foundations of software science and computation structures ; 23rd International conference, FOSSACS 2020, Held as part of the European joint conferences on theory and practice of software, ETAPS 2020, Dublin, Ireland, April 25–30, 2020, proceedings
This book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020.
Fading Foundations : Probability and the Regress Problem
This book addresses the age-old problem of infinite regresses in epistemology. How can we ever come to know something if knowing requires having good reasons, and reasons can only be good if they are backed by good reasons in turn? The problem has puzzled philosophers ever since antiquity, giving rise to what is often called Agrippa's Trilemma. The current volume approaches the old problem in a provocative and thoroughly contemporary way. Taking seriously the idea that good reasons are typically probabilistic in character, it develops and defends a new solution that challenges venerable philosophical intuitions and explains why they were mistakenly held. Key to the new solution is the phenomenon of fading foundations, according to which distant reasons are less important than those that are nearby.
Deduction, Computation, Experiment : Exploring the Effectiveness of Proof
What is a proof for? What is the characteristic use of a proof as a computation, as opposed to its use as an experiment? What is the relationship between mathematical procedures and natural processes? The essays collected in this volume address such questions from different points of view and will interest students and scholars in several branches of scientific knowledge. Some essays deal with the logical skeleton of deduction, others examine the interplay between natural systems and models of computation, yet others use significant results from the natural sciences to illustrate the character of procedures in applied mathematics. Focusing on relevant conceptual and logical issues underlying the overall quest for proving, the volume seeks to cast light on what the effectiveness of proof rests on.
Concept Lattices and Their Applications ; Fourth International Conference, CLA 2006 Tunis, Tunisia, October 30-November 1, 2006 Selected Papers
This book constitutes the refereed proceedings of the Fourth International Conference on Concept Lattices and their Applications, CLA 2006, held in Tunis, Tunisia, October 30-November 1, 2006.
Computer Science Logic ; 22nd International Workshop, CSL 2008 , 17th Annual Conference of the EACSL, Bertinoro, Italy, September 16-19, 2008. Proceedings
This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Science Logic, CSL 2008, held as the 17th Annual Conference of the EACSL in Bertinoro, Italy, in September 2008.
Automata, languages and programming ; Vol. 3580 ; 32nd International Colloquim, ICALP 2005, Lisbon, Portugal, July 11-15, 2005, Proceedings
This book constitutes the refereed proceedings of 32nd International Colloquium on Automata, Languages and Programming ICALP 2005, Lisbon, Portugal, July 11-15, 2005. including Topics Computer Science, general Mathematical Logic and Foundations Theory of Computation Software Engineering/Programming and Operating Systems Data Structures and Information Theory Data Structures
An Invitation to Abstract Mathematics
this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise.This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts.
Advances in proof-theoretic semantics
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory.
A Geometry of Approximation : Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns
A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost.
