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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.
Model and Mathematics : From the 19th to the 21st Century
This book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models.
Foundations of information and knowledge systems ; 5th International Symposium, FoIKS 2008, Pisa, Italy, February 11-15, 2008. Proceedings
This book constitutes the refereed proceedings of the 5th International Symposium on Foundations of Information and Knowledge Systems, FoIKS 2008 held in Pisa, Italy, in February 2008. The 13 revised full papers presented together with 9 revised short papers and 3 invited lectures were carefully selected during two rounds of reviewing and improvement from from 79 submissions. The papers deal with any foundational aspect of information and knowledge systems, including submissions from researchers working in fields such as discrete mathematics, logic and algebra, model theory, information theory, complexity theory, algorithmics and computation, geometry, analysis, statistics and optimisation who are interested in applying their ideas, theories and methods to research on information and knowledge systems.
Foundations of information and knowledge systems ; 4th International Symposium, FoIKS 2006, Budapest, Hungary, February 14-17, 2006, Proceedings
This book constitutes the refereed proceedings of the 4th International Symposium on Foundations of Information and Knowledge Systems, held in February 2006. The 14 revised full papers presented together with three revised short papers and one invited paper were carefully reviewed and selected from 54 submissions. Among the topics covered are the theoretical foundations of information and knowledge systems, as well as mathematical fields such as discrete mathematics, combinatorics, logics and finite model theory, and applications thereof for research on database and knowledge base theory.
Finite model theory and its applications
This book gives a broad overview of core topics of finite model theory: expressive power, descriptive complexity, and zero-one laws, together with selected applications to database theory and artificial intelligence, especially, constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, which emphasizes the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of, and hierarchies within, first order, second order, fixed point, and infinitary logics to gain insight into phenomena in complexity theory and combinatorics.
Computer science logic ; Vol. 4207 ; 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Szeged, Hungary, September 25-29, 2006, Proceedings
Coverage includes automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, automata and formal logics, modal and temporal logic, model checking, finite model theory, and more.
Computer Science Logic ; 21 International Workshop, CSL 2007, 16th Annual Conference of the EACSL, Lausanne, Switzerland, September 11-15, 2007, Proceedings
This book covers logic and games, expressiveness, games and trees, logic and deduction, lambda calculus, finite model theory, linear logic, proof theory, and game semantics.
An introduction to description logics
Designed so that domain knowledge can be described and so that computers can reason about this knowledge. DLs have recently gained increased importance since they form the logical basis of widely used ontology languages, in particular the web ontology language OWL. Written by four renowned experts, this is the first textbook on description logics. It is suitable for self-study by graduates and as the basis for a university course. Starting from a basic DL, the book introduces the reader to their syntax, semantics, reasoning problems and model theory and discusses the computational complexity of these reasoning problems and algorithms to solve them.
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.
