Hajnal Andréka and István Németi on Unity of Science

This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives.

Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. 

The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself.

• Tarskian Algebraic Logic
• Cylindric Algebras, Relation Algebras
• Guarded Fragment of First Order Logic
• Modal Logic, Modal Operators
• Institution Theory
• Decision Problems For Binary Relations
• Structuralism
• Properties of General Relativistic Spacetimes
• Emergent Spacetime
• Equivalence of Theories
• Network of Theories
• Foundational Thinking
• Computer Science, Machine Intelligence, Logic of Programs
• Semiring Provenance for Guarded Logics
• Implicit Partiality of Signature Morphisms in Institution Theory
• Query-Answering and Reasoning with Datalog+/-
• Action Axioms, Algebraically
• Adding Guarded Constructions to the (Relational) Syllogistic

• Alfréd Rényi Institute of Mathematics, Budapest, Hungary

  Judit Madarász, Gergely Székely

Judit Madarász has been working at the Alfréd Rényi Institute of Mathematics since 1998, currently in the position of Senior Research Fellow. Her research interests include logical foundations of special and general relativity, mathematical logic, and algebraic logic.

Gergely Székely has been working at the Alfréd Rényi Institute of Mathematics since 2008, currently in the position of Senior Research Fellow. His main research interests are logic-based axiomatic foundations of the special and general theories of relativity, applications of mathematical logic in physical sciences, and in connecting and comparing different theories.