Janusz Czelakowski Books

Focusing on the concept of consequence operations, this book explores recent advancements in logic, presenting a cohesive theory based on simple assumptions. It highlights the connections between algebra and logic within abstract algebraic logic, specifically addressing logics in zero-order languages. While the historical context of these ideas is noted, it is not the primary focus. The theory's applicability extends to higher-order languages, with successful integration into first-order languages, drawing on the contributions of Blok and Pigozzi.

Focusing on abstract algebraic logic, this monograph delves into commutator equations and equationally-defined commutators. It presents a thorough examination of the commutator operation linked to equational deductive systems, highlighting its logical implications within quasivarieties of algebras. The author addresses general properties of the equationally-defined commutator, explores centralization relations for relative congruences, and discusses its additivity, correspondence properties, and behavior in finitely generated quasivarieties.