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Consequence Relations
The publication of Rasiowa and Sikorski's The Mathematics of Metamathematics (1970), Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki's Theory of Logical Calculi (1988) created a niche in the field of mathematical and philosophical logic. This in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky consider the problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand. For ...
Fragments of First-Order Logic
A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first-order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite satisfiability).In contrast, the satisfiability and finite satisfiability problems are algorithmically solvable for restricted subsets---or, as we say, fragments---of first-order logic, a fact which is today of considerable interest in Computer Science. This...
Larisa Maksimova on Implication, Interpolation, and Definability
This edited volume focuses on the work of Professor Larisa Maksimova, providing a comprehensive account of her outstanding contributions to different branches of non-classical logic. The book covers themes ranging from rigorous implication, relevance and algebraic logic, to interpolation, definability and recognizability in superintuitionistic and modal logics. It features both her scientific autobiography and original contributions from experts in the field of non-classical logics. Professor Larisa Maksimova's influential work involved combining methods of algebraic and relational semantics. Readers will be able to trace both influences on her work, and the ways in which her work has influe...
Leo Esakia on Duality in Modal and Intuitionistic Logics
This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.
Logic, Language, and Computation
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 7th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2007, held in Tbilisi, Georgia, in October 2007. The 22 revised full papers included in the book were carefully reviewed and selected from numerous presentations given at the symposium. The focus of the papers is on the following topics: conceptual modeling of spatial relations, pragmatics and game theory, atypical valency phenomena, lexical typology, formal semantics and experimental evidence, exceptional quantifier scope, Georgian focussing particles, polarity and pragmatics, dynamics of belief, learning theory, inquisitive semantics, modal logic, coalgebras, computational linguistics of Georgian, type-logical grammar and cross-serial dependencies, non-monotonic logic, Japanese quantifiers, intuitionistic logic, semantics of negated nominals, word sense disambiguation, semantics of question-embedding predicates, and reciprocals and computational complexity.
Innovations and Advances in Computer Sciences and Engineering
Innovations and Advances in Computer Sciences and Engineering includes a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of Computer Science, Software Engineering, Computer Engineering, and Systems Engineering and Sciences. Innovations and Advances in Computer Sciences and Engineering includes selected papers form the conference proceedings of the International Conference on Systems, Computing Sciences and Software Engineering (SCSS 2008) which was part of the International Joint Conferences on Computer, Information and Systems Sciences and Engineering (CISSE 2008).
V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics
This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-sp...
Mathematical Reviews
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