Seminar Logic, Complexity, Games: FixedPoint Logics
WS 2023/24
Information

The complete course materials are only available on our Moodle course page.
Organisation
The presentations will take place as a block seminar at the end of the semester.
 Language: you may choose between English and German
 Length of seminar paper: around 7 pages
 Duration of presentation: 25 minutes
Content
Fixedpoint 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 firstorder logic, propositional modal logic, or conjunctive queries) by the possibility to define fixedpoints of relational operators. Fixedpoint logics come in many incarnations and variations, depending on the kind of relational operators that are used, on the kind of fixedpoints (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, fixedpoint 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 fixedpoints, 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 mucalculus 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 fixedpoint logic with the theory of infinite games.
In the seminar, we shall study the structure, the modeltheoretic properties, and the expressive power of different variants of fixedpoint logic, and explore algorithmic problems that arise in the application of such formalisms in different areas of logic and computer science.
Classification
 Informatik (B.Sc.)
 Mathematik (B.Sc.)
 Informatik (M.Sc.)
 Mathematik (M.Sc.)
 Grundlagen der Informatik (M.Sc.)
 Data Science (M.Sc.)
 Software Systems Engineering (M.Sc.)
 Media Informatics (M.Sc.)
Prerequisites
 Mathematical Logic
 for B.Sc. Computer Science: Module "Einführung in das wissenschaftliche Arbeiten (Proseminar)"
Contact
Erich Grädel, Matthias Naaf, Sophie Brinke, Lovro Mrkonjić