Seminar Logic, Complexity, Games: Fixed-point logics

SS 2015


  • 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.


Students with a subject in mathematics can apply by writing an email to seminar [AT] including their name, immatriculation no., subject of studies, no. of semesters of studies, and information about relevant modules they have passed (especially lectures from our group).


Die Veranstaltung wird als Blockseminar angeboten, die Vorträge werden am Ende des Semesters wahlweise auf deutsch oder englisch gehalten.


22. MaiGliederung
19. JuniAusarbeitung
spätestens 13. JuliFolien
13. AugustVorträge


Donnerstag, 13. August
10:0010:30Lena VollbachLFP = IFP
10:3011:00Mehri BagherihamanehBounded-Variable Fixpoint Queries are PSPACE-Complete
11:1511:45Carolin TidauThe Expressive Equivalence of LFP and PFP
11:4512:15Matthias VoitMonadic Least Fixed-Point Logic and its Two-Variable Fragments
14:0014:30 Markus Baumeister Strictness of the Alternation Hierachy of the Modal mu-Calculus
14:3015:00Oliver MajorInflationary Fixed Points in Modal Logic


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.


LFP = IFPLena VollbachWied Pakusa
Monadic Least Fixed-Point Logic and its Two-Variable FragmentsMatthias VoitWied Pakusa
The Expressive Equivalence of LFP and PFPCarolin TidauSvenja Schalthöfer
Bounded-Variable Fixpoint Queries are PSPACE-CompleteMehri BagherihamanehFaried Abu Zaid
Inflationary Fixed Points in Modal LogicOliver MajorFaried Abu Zaid
Strictness of the Alternation Hierachy of the Modal mu-Calculus Markus Baumeister Frederic Reinhardt


  • 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


  • Module Mathematical Logic
  • for B.Sc. Computer Science: Module "Einführung in das wissenschaftliche Arbeiten (Proseminar)"


Erich Grädel, Faried Abu Zaid, Wied Pakusa, Svenja Schalthöfer, Frederic Reinhardt