Algebraic ligic; investigating the logical structure of relativity theory  Page description

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Details of project

  
Identifier
43242
Type K
Principal investigator Németi, István
Title in Hungarian Algebrai logika; relativitáselmélet logikai struktúrájának vizsgálata
Title in English Algebraic ligic; investigating the logical structure of relativity theory
Panel Mathematics and Computing Science
Department or equivalent Alfréd Rényi Institute of Mathematics
Participants Andai, Attila
Andréka, Hajnal
Csirmaz, László
Etesi, Gábor
Ferenczi, Miklós
Henk, Csaba
Madarász, Judit
Sági, Gábor
Sain, Ildikó
Serény, György
Simon, András
Simon, András
Tőke, Csaba
Vályi, Sándor
Starting date 2003-01-01
Closing date 2007-12-31
Funding (in million HUF) 14.705
FTE (full time equivalent) 2.00
state closed project





 

Final report

  
Results in Hungarian
Gödel, Einstein és Tarski hagyományait kívánjuk folytatni, elmélyítve a Gödel-Einstein együttműködés eredményeit is, és folytatva Tarski tudományegyesítési programmját. Ismert, hogy a logika és a matematika modern megalapozása Gödel és Tarski úttörő munkásságára vezethető vissza. Kevésbbé ismert, hogy Gödel 1948-tól majdnem élete végéig Einsteinnel szorosan együttműködve relativitáselméleten dolgozott, ahol ugyanolyan meghökkentő új horizontokat tárt fel mint logikában, és hogy Gödel relativitáselméleti gondolatai folytatásaként fogható fel a forgó fekete lyukak mai elmélete. Ezen előzmények folytatása a jelen projektum, mely Tarskival és munkatársaival való személyes együttműködés (pl. közös könyv) keretében kezdődött. Az alapgondolat a logika, algebra, geometria, téridőelmélet és relativitáselmélet egységben való művelése. Eredményeinkből egy példa: Nagy, lassan forgó fekete lyukakról bizonyítottuk, hogy a belsejében létrejövő un. zárt időszerű görbe (időhurok) létrejöttére vonatkozó szokásos irodalmi magyarázatok tévesek. Nem az un. drag effect (mozgó anyag magával vonszolja a téridőt) okozza a zárt görbéket, hanem egy egészen más jellegű hatás: a fénykúpok kinyílása a forgással ellentétes irányban. Az eredmény a General Relativity and Gravitation című folyóiratban jelenik meg.
Results in English
The reported project intends to continue traditions of Gödel, Einstein and Tarski continuing the spirit of the Gödel-Einstein collaboration and pursuing Tarski’s programme for unifying science. Modern logic and meta-mathematics was created (basically) by Gödel and Tarski. It is less well known that beginning with 1948 Gödel spent much time with Einstein and worked on relativity theory. Of course, he remained a logician in spirit. Gödel obtained fundamental breakthroughs in relativity like his ones in logic and foundations. The theory of general relativistic spacetimes not admitting a global Time was initiated by Gödel, and came to full blossom during the renaissance of black hole physics during the last 25 years. The present project was originally started in personal cooperation with Tarski and his collaborators. The idea is to study logic, algebra, geometry, spacetime theory and relativity in a strong unity. A sample result of ours: We proved about big, slowly rotating black holes that the usual explanation in the literature of why such black holes contain a closed timelike curve (CTC) is flawed. Namely, it is not the gravitational frame dragging effect which creates CTCs, instead, there is a completely different kind of effect in action there: ligh cones open up in the direction opposite to that of the rotation of the source and this goes on to such an extreme extent that CTCs are created. Our paper on this appears in the journal General Relativity and Gravitation.
Full text http://real.mtak.hu/988/
Decision
Yes





 

List of publications

  
Andai A.: Információgeometria a kvantummechanikában., Doktori Értekezés, BME. (iv)+220 old., 2003
Andréka H; Madarász JX; Németi I; Székely G.: A logical investigation of inertial and accelerated observers in flat space-times., In: Kalmár Workshop on Logic and Computer Science, Gécseg F. Csirik J. és Turán Gy. szerk., Department of Informatics, University of Szeged, Szeged, Hungary. 45-57., 2003
Andréka H; Madarász JX; Németi I.: Logical analysis of relativity theories., In: Hendricks V, Neuhaus V, Pedersen S.A, Scheffler U, Wansing H. (ed.) First-order logic revisited, Berlin: Logos Verlag. pp.7-36., 2004
Andréka H; Madarász JX; Németi I.: Logical axiomatizations of space-time. Samples from the literature., In: Prékopa, A. és Molnár, E. (ed.) Non-Euclidean geometries:János Bolyai memorial volume. Mathematics and Its Applications Vol. 581. Springer pp.155-185., 2006
Henk Cs.: Characterizing representability of Jónsson dynamic algebras parametrized by free Kleene algebras., In: Kalmár Workshop on Logic and Computer Science, Gécseg F. Csirik J. Turán Gy. (ed.), Department of Informatics, University of Szeged, Szeged, Hungary. pp.99-105., 2003
Madarász JX; Németi I; Tőke Cs.: On generalizing the logic-approach to space-time towards general relativity: first steps., In: Hendricks V. Neuhaus F. Pedersen SA. Scheffler U. Wansing H. (ed.) First-order logic revisited, Berlin: Logos Verlag. pp.225-268., 2004
Madarász JX; Tőke Cs.: Duality between observational and theoretical concepts in relativity theory analysed by FOL and definability theory., In: Kalmár Workshop on Logic and Computer Science, Gécseg F. Csirik J. Turán Gy. (ed.), Department of Informatics, University of Szeged, Szeged, Hungary. pp.133-143., 2003
Serény Gy.: Boolos-style proofs of limitative theorems., Mathematical Logic Quarterly 50(2): 211-216., 2004
Andréka H; Comer SD; Madarász JX; Németi I; Sayed-Ahmed T.: Epimorphisms in cylindric algebras., Közlésre elfogadva. Algebra Universalis, 2007
Andréka H; Madarász JX; Németi I.: Algebras of relations of various ranks, some current trends and applications., Journal of Relational Methods in Computer Science 1: 27-49., 2004
Andréka H; Madarász JX; Németi I.: Mutual definability does not imply definitional equivalence, a simple example., Math. Log. Quart. 51,6 : 591-597., 2005
Ferenczi M; Pataricza A; Rónyai L; szerkesztők.: Formal methods in computing., Akadémia Kiadó, Budapest, 425 oldal, 2005
Ferenczi M.: Classical and non-classical logics., In: Formal Methods in Computing, ed. Ferenczi, M., Pataricza, A., Rónyai, L., Akadémiai Kiadó, Budapest 2005. pp.97-155., 2005
Ferenczi M.: Probabilities on first order models., Publications de l’Institute Mathematique (Beograd) 78(92), pp.107-115., 2005
Ferenczi M; Sági G.: On Some Developments in the Representation Theory of Cylindric-Like Algebras,, Algebra Universalis vol 55, pp.345-353., 2006
Hogarth M: Conventionality of Simultaneity: Malament’s result revisited, Foundations of Physics Letters 18,5: 491-497, 2005
Vályi S; Mecsei Z.: A Gentzen-style extension of natural deduction – adjusted for undergraduate informatics studies., Proceedings of Informatics in Higher Education 2005, Debrecen. Pethő A, Herdon M. szerk., 5 oldal., 2005
Serény Gy.: The Liar cannot be solved., In: Truth, Unity and The Liar. (eds. Sh. Raman, T. Tulenheimo, E. Genot). Invited contributed paper, közlésre elfogadva., 2007
Andai A.: On the curvature of the quantum state space with pull-back metrics., Linear Algebra and Its Applications 423: 287-304, 2007
Etesi G.: Homotopic classification of Yang-Mills vacua taking into account causality., Int. Journ. Theor. Phys. 46: 832-847., 2007
Etesi G.: Gravitational interpretation of the Hitchin equations., Journ. Geom. Phys. 57: 1778-1788., 2007
Ferenczi M.: Finitary polyadic algebras from cylindric algebras., Studia Logica 87, pp.1-11., 2007
Ferenczi M.: On cylindric algebras satisfying the merry-go-round properties., Logic Journal of IGPL 15,2: 183-199., 2007
Madarász JX; Németi I; Székely G.: First-order logic foundation of relativity theories., In: New logics for the XXIst century. Vol II. Mathematical Problems from Applied Logics, Springer. pp.217-252., 2007
Serény Gy.: The diagonal lemma as the formalized Grelling paradox., In: Gödel Centenary 2006, M. Baaz, N. Preining eds., Collegium Logicum 9, Kurt Gödel Society, Vienna. pp.63-66., 2006
Simon A.: Connections between quasi-projective relation algebras and cylindric algebras., Algebra Universalis 56,3-4: 263-301., 2007
Nagy B; Vályi S.: Visual reasoning by generalized interval-values and interval temporal logic., CEUR Workshop Proceedings vol 274, ISSN 1613-0073, pp.13-26., 2007
Madarász JX; Sayed-Ahmed T.: Amalgamation, Interpolation and epimorphisms in algebraic logic., Algebra Universalis 56,2: 179-210., 2007
Németi I; Andréka H.: Can general relativistic computers break the Turing barrier?, Logical Approaches to Computational Barriers, A. Beckmann, U. Berger, B. Löwe, J.V. Tucker szerk., Lecture Notes in Computer Science Springer, Berlin. pp.398-412., 2006
Nagy B; Vályi S.: Solving a PSPACE-complete problem by a linear interval-valued computation., In: Computability in Europe 2006: Logical Approaches to Computational Barriers., University of Swansea, A. Beckmann, U. Berger, B. Löwe, J. Tucker eds., pp.216-225., 2006
Nagy B; Vályi S.: Interval-valued computations without the product operator., In: Proc. 7th International Conference on Applied Informatics. közlésre elfogadva. 7 old., 2007
Nagy B; Vályi S.: Interval-valued computating as a visual reasoning system., In: Proc. 13th International Conference on Distributed Multimedia Systems. pp.247-250., 2007
Vályi S.: On monadic second-order theories of the causal connectabilitz relation., Journal of Philosophical Logic, közlésre elfogadva. 12 old., 2007
Vályi S.: Investigations into non-classical logic - axiomatizability of spatio-temporal theories and complexity of interval-valued computations., PhD Dissertation. Doctoral School in Mathematics and Computer Science of University of Debrecen., 2007
Andréka H; Madarász JX; Németi I; Székely G.: Axiomatizing relativistic dynamics without conservation postulates., Studia Logica, megjelenés alatt. 20 old., 2007
Andai A.: Monotone Riemannian metrics on density matrices with non-monotone scalar curvature., Journal of Mathematical Physics 44:3675-3688, 2003
Andréka, H. Madarász, J.X. Németi, I.: Logic of spacetime and relativity., In: Handbook of Spatial Logics. Eds: Aiello, M. Pratt-Hartmann, I. and van Benthem, J. Springer-Verlag. pp.607-701., 2007
Andréka H; Németi I; Sayed-Ahmed T.: Omitting types for finite variable fragments and complete representations of algebras., Journal of Symbolic Logic, megjelenés alatt. 34 old., 2007
Andréka H; Németi I; Wüthrich C.: A twist in the geometry of rotating black holes: seeking the cause of acausality., General Relativity and Gravitation, megjelenés alatt. 21 old., 2007
Etesi G.: The topology of asymptotically locally flat gravitational instantons., Phys. Lett. B641, 461-465., 2006
Etesi G; Jardim M.: Moduli spaces of self-dual connections over asymptotically locally flat gravitational instantons., Commun. Math. Phys., közlésre elfogadva., 2007
Hogarth M.: Deciding arithmetic using SAD computers., Brit. J. Phil. Sci. 55: 681-691., 2004
Madarász JX; Németi I; Székely G.: Twin Paradox and the logical foundation of relativity theory., Foundation of Physics vol.36,5. pp.681-714., 2006
Nagy B; Vályi S.: Interval-valued computations and their connection to PSPACE., Theoretical Computer Science, közlésre elfogadva. 22 old., 2007
Németi I; Dávid Gy.: Relativistic computers and the Turing barrier., Journal of Applied Mathematics and Computation vol.178. pp.118-142., 2006



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