Seminar Logik, Komplexität, Spiele: Fixed-point logics
SS 2015
Aktuelles
- Die Vorträge finden im Raum 5056 (2356|056) (Seminarraum am AH V) statt.
- Die von der Fachgruppe Informatik verfassten ethischen Richtlinien für das Verfassen wissenschaftlicher Arbeiten sind hier zu finden und gelten selbstverständlich auch für dieses Seminar.
Anmeldung
- Studierende in Mathematik-Studiengängen können sich per Email an seminar [AT] logic.rwth-aachen.de bewerben. Bitte geben Sie dazu Ihren vollständigen Namen, Matrikelnummer, Studiengang, Fachsemester und Ihre Vorkenntnisse (insbesondere an unserem Lehrgebiet besuchte Vorlesungen) an.
- Studierende in Informatik-Studiengängen können sich über die zentrale Vergabe von Seminarplätzen bewerben.
Organisation
Die Veranstaltung wird als Blockseminar angeboten.Zeitplan
| 22. Mai | Gliederung |
| 19. Juni | Ausarbeitung |
| spätestens 13. Juli | Folien |
| 13. August | Vorträge |
Programm
| Donnerstag, 13. August | ||||
| – | Lena Vollbach | LFP = IFP | ||
| – | Mehri Bagherihamaneh | Bounded-Variable Fixpoint Queries are PSPACE-Complete | ||
| – | Carolin Tidau | The Expressive Equivalence of LFP and PFP | ||
| – | Matthias Voit | Monadic Least Fixed-Point Logic and its Two-Variable Fragments | ||
| – | Markus Baumeister | Strictness of the Alternation Hierachy of the Modal mu-Calculus | ||
| – | Oliver Major | Inflationary Fixed Points in Modal Logic | ||
Inhalt
Fixed-point logics are of fundamental importance in many branches of logic and computer science, including finite model theory, verification, knowledge representation, complexity theory, and databases. They extend a basic logical formalism (such as first-order logic, propositional modal logic, or conjunctive queries) by the possibility to define fixed-points of relational operators. Fixed-point logic come in many incarnations and variations, depending on the kind of relational operators that are used, on the kind of fixed-points (least and greatest fixed points, inflationary and deflationary fixed points, partial fixed points, simultaneous inductions, etc.,) and on the combination and interaction with other logical operators.
In finite model theory, fixed-point logics play a central role since they capture recursion and unbounded iteration in a natural and powerful way, and are of fundamental importance in the quest of logics that capture complexity classes. In database theory, query languages based on fixed-points, such as Datalog and its extensions, are of interest since they allow to define queries that are not expressible in basic languages like SQL. The modal mu-calculus is an important formalism for the specification and verification and encompasses most of the commonly used modal and temporal logics used in that area. There also is a very close and important relationship of fixed-point logic with the theory of infinite games.
In the seminar, we shall study the structure, the model-theoretic properties, and the expressive power of different variants of fixed-point logic, and explore algorithmic problems that arise in the application of such formalisms in different areas of logic and computer science.
Themen
| Thema | Vortragende(r) | Betreuer(in) |
| LFP = IFP | Lena Vollbach | Wied Pakusa |
| Monadic Least Fixed-Point Logic and its Two-Variable Fragments | Matthias Voit | Wied Pakusa |
| The Expressive Equivalence of LFP and PFP | Carolin Tidau | Svenja Schalthöfer |
| Bounded-Variable Fixpoint Queries are PSPACE-Complete | Mehri Bagherihamaneh | Faried Abu Zaid |
| Inflationary Fixed Points in Modal Logic | Oliver Major | Faried Abu Zaid |
| Strictness of the Alternation Hierachy of the Modal mu-Calculus | Markus Baumeister | Frederic Reinhardt |
Zuordnung
- Informatik (B.Sc.)/Seminar Informatik
- Mathematik (B.Sc.)/Seminar: Logik, Komplexität, Spiele
- Informatik (M.Sc.)/Seminar Theoretische Informatik
- Mathematik (M.Sc.)/Seminar: Logik, Komplexität, Spiele (Reine Mathematik)
- Informatik (S II)
- Mathematik (S II)/Hauptstudium/Modul Algebra
- Mathematik (S II)/Hauptstudium/Modul Angewandte Mathematik
Voraussetzungen
- Modul Mathematische Logik
- für B.Sc. Informatik: bestandenes Modul "Einführung in das wissenschaftliche Arbeiten (Proseminar)"
Rückfragen
Erich Grädel, Faried Abu Zaid, Wied Pakusa, Svenja Schalthöfer, Frederic Reinhardt