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Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi-dimensionality in modal logic is a technical one: we call a modal formalism multi-dimensional if, in its intended semantics, the universe of a model consists of states that are tuples over some more basic set.) This book treats such multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. We will define and discuss a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation. Although the book will be mathematical in spirit, we take care to give motivations from the disciplines mentioned earlier on.

Modality (Logic) --- Modalité (Logique) --- Modality (Logic). --- Modalité (Logique) --- Logic. --- Mathematical logic. --- Computational linguistics. --- Mathematical Logic and Foundations. --- Computational Linguistics. --- Automatic language processing --- Language and languages --- Language data processing --- Linguistics --- Natural language processing (Linguistics) --- Applied linguistics --- Cross-language information retrieval --- Mathematical linguistics --- Multilingual computing --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Data processing --- Methodology --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation

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We address the problem of publishing parliamentary proceedings in a digital sustainable manner. We give an extensive requirements analysis, and based on that propose a uniform XML format. We evaluated our approach by collecting and automatically processing proceedings from six parliaments spanning almost 200 years in total. Most of this data is real legacy data consisting of scanned and OCRed documents. The approach scales very well and produces high quality data. All documents are transformed into UTF-8 encoded XML files with extensive metadata in Dublin Core standard. The text itself is divided into pages which are divided into paragraphs. Every document, page and paragraph has a unique URN which resolves to a web page. Every page element in the XML files is connected to a facsimile image of that page in PDF or JPEG format. We created a viewer in which both versions can be inspected simultaneously. A search-engine for the complete collection is available online.

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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. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful technique for analyzing the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and tree-width, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research in finite model theory, and all readers will experience the excitement of a vibrant area of application of logic to computer science.

Finite model theory. --- Computational complexity. --- Constraint databases. --- Databases --- Complexity, Computational --- Electronic data processing --- Machine theory --- Computer science --- Model theory --- Mathematics --- Information theory. --- Computer science. --- Software engineering. --- Logic design. --- Database management. --- Theory of Computation. --- Mathematical Logic and Formal Languages. --- Software Engineering. --- Computation by Abstract Devices. --- Logics and Meanings of Programs. --- Database Management. --- Data base management --- Data services (Database management) --- Database management services --- DBMS (Computer science) --- Generalized data management systems --- Services, Database management --- Systems, Database management --- Systems, Generalized database management --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Computer software engineering --- Engineering --- Informatics --- Science --- Communication theory --- Communication --- Cybernetics --- Computers. --- Mathematical logic. --- Computer logic. --- Computer science logic --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Calculators --- Cyberspace

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