Many-valued Semantics and Modal Logics: Essays in Honour of Yuriy Vasilievich Ivlev

This volume is a collection of essays related to the work of Professor Yuriy Vasilievich Ivlev, a distinguished Russian logician and philosopher renowned for his expertise in many-valued and modal logics. Notably, his groundbreaking work on quasi-matrices for logics, now recognized as non-deterministic matrices and non-deterministic semantics, emerged in the 1970s. From a philosophical standpoint, Ivlev’s research delves into the formal analysis of indeterminacy, offering a logical framework to understand how sequences of indeterminate events can yield determinate outcomes. The volume follows two complementary lines of research. Firstly, it serves as a platform for the exploration and discussion of Ivlev’s seminal contributions to the algebraic characterization of both normal and non-normal modal logics, aimed at making these insights accessible to an international audience. Secondly, it features contributions from esteemed logicians and philosophers worldwide, offering diverseperspectives on the logical analysis of indeterminacy. This comprehensive volume will appeal to scholars and researchers in logic, philosophy, and mathematics who are engaged in the study of many-valued and modal methodologies for modeling situations of indeterminacy.

Part I: Translation of Quasi-matrix (quasi-functional) logic.- 1. Quasi-matrix (quasi-functional) logic (Yuriy Vasilievich Ivlev).- Part II: Many-valued logics with indeterminacy.- 2. A Cartography of LFIs and Truth (Eduardo Barrio and Federico Pailos).- 3. On Non-deterministic Functional Completeness (Arnon Avron).- 4. Non-deterministic logic of generalized classical truth values (Oleg Grigoriev and Yaroslav Petrukhin).- 5. Tableau systems for some Ivlev-like (quantified) modal logics (Marcelo E. Coniglio, Luis Fari˜nas del Cerro, and Newton M. Peron).- 6. Plurivaluationism, Semantic Nondeterminism and Communication (Nicholas J.J. Smith).- Part III: Many-valued and modal logics.- 7. Algebras and relational frames for G¨odel modal logic and some of its extensions (Tommaso Flaminio, Lluis Godo, Paula Mench´on, and Ricardo O. Rodriguez).- 8. Many-Valued Modalities and Paraconsistency (Juliana Bueno-Soler, Walter Carnielli, and Abilio Rodrigues).- 9. On Ivlev’s semantics for modality (Hitoshi Omori and Daniel Skurt).- 10. Valuation semantics for some systems of non-normal modal logic (Cezar A. Mortari).- 11. Efficient reasoning about knowledge and common knowledge (Andreas Herzig and Elise Perrotin).