Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science

✍ Scribed by Janusz Czelakowski

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 476
• Series: Outstanding Contributions to Logic 16
• Edition: 1st ed.
• Category: Library

✦ Synopsis

This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life.

It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.

✦ Table of Contents

Front Matter ....Pages i-xxxiii
A Mathematical Life (Don Pigozzi)....Pages 1-51
Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic (Hugo Albuquerque, Josep Maria Font, Ramon Jansana, Tommaso Moraschini)....Pages 53-79
Deduction-Detachment Theorem and Gentzen-Style Deductive Systems (Sergey Babenyshev)....Pages 81-101
Introducing Boolean Semilattices (Clifford Bergman)....Pages 103-130
The Equationally-Defined Commutator in Quasivarieties Generated by Two-Element Algebras (Janusz Czelakowski)....Pages 131-165
A short overview of Hidden Logic (Isabel Ferreirim, Manuel A. Martins)....Pages 167-201
Absorption and directed Jónsson terms (Alexandr Kazda, Marcin Kozik, Ralph McKenzie, Matthew Moore)....Pages 203-220
Relatively congruence modular quasivarieties of modules (Keith A. Kearnes)....Pages 221-232
The computational complexity of deciding whether a finite algebra generates a minimal variety (George F. McNulty)....Pages 233-256
Characterization of protoalgebraic k-deductive systems (Katarzyna Pałasińska)....Pages 257-271
Diagrammatic duality (Anna B. Romanowska, Jonathan D.H. Smith)....Pages 273-295
Boolean product representations of algebras via binary polynomials (Antonino Salibra, Antonio Ledda, Francesco Paoli)....Pages 297-321
Paraconsistent constructive logic with strong negation as a contraction-free relevant logic (Matthew Spinks, Robert Veroff)....Pages 323-379
Possible classification of finite-dimensional compact Hausdorff topological algebras (Walter Taylor)....Pages 381-420
Categorical Abstract Algebraic Logic: Compatibility Operators and Correspondence Theorems (George Voutsadakis)....Pages 421-454

✦ Subjects

Philosophy; Logic; Mathematical Logic and Foundations; Mathematical Logic and Formal Languages