Towards Mathematical Philosophy: Papers from the Studia Logica conference Trends in Logic IV (Trends in Logic)

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. area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic. "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 prepositional 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."--Jacket Front Matter....Pages i-xiii From Logic to Mathematical Philosophy....Pages 1-7 Commutativity of Quantifiers in Varying-Domain Kripke Models....Pages 9-30 The Method of Tree-Hypersequents for Modal Propositional Logic....Pages 31-51 All Splitting Logics in the Lattice NExt (KTB)....Pages 53-67 A Temporal Logic of Normative Systems....Pages 69-106 Reasoning with Justifications....Pages 107-123 Monotone Relations, Fixed Points and Recursive Definitions....Pages 125-164 Processing Information from a Set of Sources....Pages 165-186 The Classical Model Existence Theorem in Subclassical Predicate Logics I....Pages 187-199 Weak Implicational Logics Related to the Lambek Calculus—Gentzen versus Hilbert Formalisms....Pages 201-212 Faithful and Invariant Conditional Probability in Łukasiewicz Logic....Pages 213-232 A Fuzzy Logic Approach to Non-Scalar Hedges....Pages 233-248 The Procedures for Belief Revision....Pages 249-268 Shifting Priorities: Simple Representations for Twenty-Seven Iterated Theory Change Operators....Pages 269-296 The Coherence of Theories—Dependencies and Weights....Pages 297-318 On Meta-Knowledge and Truth....Pages 319-343 Contains a collection of articles applying methods of logic or those of mathematics to solve problems, some of which come from logic itself, others from other sciences. This title discusses the problems that range from the structure of lattices of normal and other modal propositional logics to the semantics of quantified modal logic.