This volume contains a collection of articles applying methods of logic or, more generally, of mathematics to solve problems, some of which come from logic itself, others from other sciences. Its range of subjects is far from complete, but broadly representative. The first group of papers in this volume consists of contributions to pure and applied modal logic. The problems discussed here range from the structure of lattices of normal and other modal propositional logics to modal proof theory and to the semantics of quantified modal logic. The second group of papers deals with Many-valued logics - an extensive domain of strictly logical investigations rooting in philosophical questions concerning the nature of logical values. Logical investigations in cognitive science have successfully utilized methods and systems of belief revision, non-monotonic logic and dynamic epistemic logic. Towards Mathematical Philosophy deals with focal issues of belief revision. The volume concludes with contributions which may be seen to belong to the field of formal epistemology, the area applying logical, probabilistic, game-theoretic and other formal methods to problems and issues in epistemology and philosophy of science, such as those concerning anti-realism, skepticism, theory comparison and theory choice, justification, sources of knowledge and learning theories. TOC:From Logic to Mathematical Philosophy; David Makinson, Jacek Malinowski, Heinrich Wansing.- Commutativity of Quantifiers in Varying-Domain Kripke Models; Rob Goldblatt, Ian Hodkinson.- The Method of Tree-hypersequents for Modal Propositional Logic; Francesca Poggiolesi.- All Splitting Logics in the Lattice NExt(KTB); Tomasz Kowalski, Yukata Miyazaki.- A Temporal Logic of Normative Systems; Thomas Ågotnes, Wiebe van der Hoek, Juan A. Rodríguez-Aguilar, Carles Sierra, Michael Wooldridge.- Reasoning with Justifications; Melvin Fitting.- Monotone Relations, Fixed Points, and Recursive Definitions; Janusz Czelakowski.- Processing Information from a Set of Sources; A. Avron, J. Ben-Naim, B. Konikowska.- The Classical Model Existence Theorem in Subclassical Predicate Logics I; Jui-Lin Lee.- Weak Implicational Logics Related to the Lambek Calculus -- Gentzen versus Hilbert Formalisms; Wojciech Zielonka.- Faithful and Invariant Conditional Probability in Lukasiewicz Logic; Daniele Mundici.- A Fuzzy Logic Approach to Non-scalar Hedges; Stephan van der Waart van Gulik.- The Procedures for Belief Revision; Piotr Lukowski.- Shifting Priorities: Simple Representations for Twenty-seven Iterated Theory Change Operators; Hans Rott.- The Coherence of Theories -- Dependencies and Weights; Jason Jingshi Li, Rex Bing Hung Kwok, Norman Foo.- On Meta-knowledge and Truth; Urszula Wybraniec-Skardowska.
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