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 engineeringand Maxwells equations to a complex system of computer programs for designing Hungarys 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.
Part I: Computer Science, Machine Intelligence, Logic of Programs.-
Chapter
1. Semiring Provenance for Guarded Logics (K. M. Dannert).
Chapter
2. Implicit Partiality of Signature Morphisms in Institution Theory (R.
Diaconescu).
Chapter
3. An Overview of Query-Answering and Reasoning with
Datalog+/- (G. Gottlob).
Chapter
4. Action Axioms, Algebraically (V.
Pratt).
Chapter
5. Adding Guarded Constructions to the (Relational)
Syllogistic (I. Pratt-Hartmann).- Chapter 6. tba (J. Tucker).- Part II .
Algebraic Logic, Algebra, Logic.- Chapter 7.- tba (J. Benthem).
Chapter
8.
Decomposing the discriminator in the semilattice of modal operators (I.
Duentsch, W. Dzik, E. Orlowska).
Chapter
9. Generalising Grzegorczyks logic
by bounding cluster size (R. Goldblatt).
Chapter
10. Undecidable decision
problems for binary relations (Hirsch-Hodkinson-Jackson).-
Chapter
11.
Relation algebras, residuated lattices and algebraic logic (P. Jipsen).-
Chapter
12. On canonical relativized relation and cylindric set algebras
(R.D. Maddux).
Chapter
13. Algebraic logic and logic geometry defined in
universal algebra (B. PLotkin, E. Plotkin).-Chapter
14. Universal algebra as
a foreign language (V. Pratt).
Chapter
15. A brief history of Tarskian
algebraic logic as enhanced by the outstanding contributions of Andreka and
Nemeti (T. Sayed-Ahmed).- Part III. Relativity Theory, spacetime,
methodology of science.
Chapter
16. Freeing structuralism from model theory
(N. Dewar).
Chapter
17. Foundational thinking (H. Friedman).
Chapter
18. In
the footsteps of Hilbert: the logical foundations of theories in physics (G.
Formica, M. Friend).
Chapter
19. The network of theories (H. Halvorson).-
Chapter
20. Internal and external properties of spacetime (J.B. Manchak).-
Chapter
21. Why not categorical equivalence? (Weatherall).
Chapter
22. Time
travelling in emergent spacetime (C. Wuthrich).
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.
