Riassunto
The book is divided into eight parts whose topics are chosen to emphasize application areas of logic, in particular those related to soft computing. Each part demonstrates possible application of logical methods to problems in the respective areas. The book presents a broad variety of fields and issues in which logic provides conceptual, technical or methodological tool. In particular, important topics in foundations of soft computing, including fuzzy logic, multiple-valued logic, theories of inconsistency and ambiguity, theory of rough sets, theories of incomplete information are studied. The book may be seen as a resource to which readers can turn for research horizons and ideas on how logical models and methods can be developed and applied. It is a source for anyone who needs broad perspective on a role of applied logic and a better understanding of logical methods and their applications. All the contributions present new and original results.
Contenuti
M. Fitting: Foreword: A Tribute to Professor Helena Rasiowa; E. Orlowska: Preface.- Logic in a Philosophical Perspective: D. van Dalen: The Role of Language and Logic in Brouwer's Work; R. Murawski: On New Trends in the Philosophy of Mathematics; J. Wolenski: Logic from a Metalogical Point of View.- Aspects of Modality: J. van Benthem: Modal Foundations of Predicate Logic; G. Gottlob: Review of a Carnapian Extension of S5; G. Mints: A Completeness Proof for Propositional S4 in Cantor Spaces; A. Nonnengart, A. Szalas: A Fixpoint Approach to Second-order Quantifier Elimination with Applications to Correspondence Theory; Y. Venema, M. Marx: A Modal Logic of Relations; with Appendix by R. Hirsch, I. Hodkinson, M. Marx, S. Mikulas, M. Reynolds: Mosaics and Step-by-step; F. Wolter, M. Zakharyaschev: Intuitionistic Modal Logics as Fragments of Classical Bimodal Logics.- Topics in Many-Valued, Intermediate and Relevant Logics: L. Gordeev: Reduction Calculi for Post Logics; S. Gottwald: On the Rule of Syllogism for Fuzzy Implication; D. Skvortsov: On Prucnal's Theorem; A. Urquhart: Beth's Definability Theorem in Relevant Logics.- Logic and Arithmetic: Z. Adamowicz: Non-codability of Restricted Sigma1 Truth; D. de Jongh, D. Pianigini: Solution of a Problem of David Gaspari; A. Visser: Interpretations over Heyting's Arithmetic.- Logic and Computer Science: M. Bialasik, B. Konikowska: A Logic for Nondeterminstic Specifications; C. Brink, J. Goslett: Propositional Logic, Powerdomains and Information; R. Caferra, N. Peltier:Disinference Rules, Model Building and Abduction; W. MacCaull: Relational Tableaux for Tree Models, Language Models and Information Networks; S. Demri, E. Orlowska: Informational Representability of Models for Information Logics; E. de Kogel, H. de Swart: An Exercise in Relational Algebra: Reduction in Programming Languages; Z. Stachniak: Polarity Strategies for Resolution Logics.- Handling Inconsistency: D. Batens: Inconsistency Adaptive Logics; S. Benferhat, D. Dubois, H. Prade: Some Syntactic Approaches to the Handling of Inconsistent Knowledge Bases: A Comparative Study 2: The Prioritized Case; M. De Glas: Pseudoconsistent Logic: Towards a Formal Framework for Handling Contradictions.- Methodology of Formal Systems: K. Dosen: On Passing from Singular to Plural Consequences; M. Krynicki, M. Mostowski: Ambiguous Quantifiers; V.V. Rybakov: Logics of Schemes for First-Order Theories and Admissible Rules; P. Wojtylak: 2-sat is not Equivalent to Booelan Prime Ideal Theorem.- Algebraic Logic: K. Halkowska: Lattices of Equational Theories of P-compatible Varieties; L. Iturrioz: Bilinear Logic and Grishin Algebras; R.D. Maddux: Relation Algebras of Formulas; H. Ono: Algebraic Semantics for Predicate Logics and Their Completeness; P. Pagliani: Algebraic Models and Proof Analysis: A Siple Case Study; I. Sain, I. Németi: Fork Algebras in Usual and in Non-well-founded Set Theories (An Overview).
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