Larisa Maksimova on Implication, Interpolation, and Definability

Description

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 influenced other logicians. In the historical part of this book, it is possible to trace important milestones in Maksimova’s career. Early on, she developed an algebraic semantics for relevance logics and relational semantics for the logic of entailment. Later, Maksimova discovered that among the continuum of superintuitionisitc logics there are exactly three pretabular logics. She went on to obtain results on the decidability of tabularity and local tabularity problems for superintuitionistic logics and for extensions of S4. Further investigations by Maksimova were aimed at the study of fundamental properties of logical systems (different versions of interpolation and definability, disjunction property, etc.) in big classes of logics, and on decidability and recognizability of such properties. To this end she determined a powerful combination of algebraic and semantic methods, which essentially determine the modern state of investigations in the area, as can be seen in the later chapters of this book authored by leading experts in non-classical logics. These original contributions bring the reader up to date on the very latest work in this field. Front Matter ....Pages i-xii Maksimova, Relevance and the Study of Lattices of Non-classical Logics (Sergei Odintsov)....Pages 1-20 A Short Scientific Autobiography (Larisa Maksimova)....Pages 21-32 Larisa Maksimova’s Early Contributions to Relevance Logic (Katalin Bimbó, J. Michael Dunn)....Pages 33-60 A Note on Strictly Positive Logics and Word Rewriting Systems (Lev Beklemishev)....Pages 61-70 Characteristic Formulas Over Intermediate Logics (Alex Citkin)....Pages 71-98 A Generalization of Maksimova’s Criterion for the Disjunction Property (Alex Citkin)....Pages 99-115 Rasiowa–Sikorski Sets and Forcing (Janusz Czelakowski)....Pages 117-153 \(\mu \)-Levels of Interpolation (Giovanna D’Agostino)....Pages 155-170 Decidability of Some Interpolation Properties for Weakly Transitive Modal Logics (Anastasia Karpenko)....Pages 171-183 Lattice NExtS4 from the Embedding Theorem Viewpoint (Alexei Muravitsky)....Pages 185-218 Linear Temporal Logic with Non-transitive Time, Algorithms for Decidability and Verification of Admissibility (Vladimir V. Rybakov)....Pages 219-243 Segerberg Squares of Modal Logics and Theories of Relation Algebras (Valentin Shehtman)....Pages 245-296 On Algebraisation of Superintuitionistic Predicate Logics (Dmitry Tishkovsky)....Pages 297-317 Dummett Logic, Irreflexive Modality and Novikov Completeness (Alexander Yashin)....Pages 319-337 On Linear Logic of Knowledge and Time (Veta F. Yun)....Pages 339-349 Back Matter ....Pages 351-371