Course Contents
The course deals with the modelling of knowledge and information in mathematical logic, fucusing on logical languages with extensional semantics over suitably designed structures for the representation of facts, knowledge about facts, (imperfect) information, distributed information, common knowledge, information updates, etc.
Approaches to be dealt with range from classical Kripke semantics (in classical modal logics) to variations involving team semantics (for imperfect information and information updates) with new logical primitives. Primary focus is on the model-theoretic investigation of the expressive power of the resulting logics, as well as the semantic justification of reasoning principles and their axiomatics.
Some main ingredients and themes:
Kripke semantics for modal logics;
bisimulation techniques: games and expressive power;
modal logic as a fragment of first-order logic;
classical correspondence theory;
finite model theory of modal logics;
relevant extensions of basic modal logic (e.g. modal µ-calculus, guarded logics);
common knowledge and public announcement;
team semantics and team properties: dependence/independence, inklusion/exclusion;
propositional, modal and first-order team logics;
model-theoretic games and equivalences;
relationships with second-order logic;
relevant fragments of first- and second-order logic.
Literature
Textbook sources (among others):
Blackburn, de Rijke, Venema: Modal Logic
Goranko, Otto: Model Theory of Modal Logics, in:
Handbook of Modal Logic, Blackburn, van Benthem, Wolter (eds) (2007)
Vaananen: Dependence Logic (2007)
Abramsky, Kontinen, Vaananen, Vollmer (eds): Dependence Logic (2016)
Preconditions
standard prerequisite: Introduction to Mathematical Logic
Additional Information
due to substantial overlap with modules "Modal Logics" and "Logics with Team Semantics"
this new 4+2 module can usually not be examined in combination with those two 2+1 modules
Online Offerings
moodle
The course deals with the modelling of knowledge and information in mathematical logic, fucusing on logical languages with extensional semantics over suitably designed structures for the representation of facts, knowledge about facts, (imperfect) information, distributed information, common knowledge, information updates, etc.
Approaches to be dealt with range from classical Kripke semantics (in classical modal logics) to variations involving team semantics (for imperfect information and information updates) with new logical primitives. Primary focus is on the model-theoretic investigation of the expressive power of the resulting logics, as well as the semantic justification of reasoning principles and their axiomatics.
Some main ingredients and themes:
Kripke semantics for modal logics;
bisimulation techniques: games and expressive power;
modal logic as a fragment of first-order logic;
classical correspondence theory;
finite model theory of modal logics;
relevant extensions of basic modal logic (e.g. modal µ-calculus, guarded logics);
common knowledge and public announcement;
team semantics and team properties: dependence/independence, inklusion/exclusion;
propositional, modal and first-order team logics;
model-theoretic games and equivalences;
relationships with second-order logic;
relevant fragments of first- and second-order logic.
Literature
Textbook sources (among others):
Blackburn, de Rijke, Venema: Modal Logic
Goranko, Otto: Model Theory of Modal Logics, in:
Handbook of Modal Logic, Blackburn, van Benthem, Wolter (eds) (2007)
Vaananen: Dependence Logic (2007)
Abramsky, Kontinen, Vaananen, Vollmer (eds): Dependence Logic (2016)
Preconditions
standard prerequisite: Introduction to Mathematical Logic
Additional Information
due to substantial overlap with modules "Modal Logics" and "Logics with Team Semantics"
this new 4+2 module can usually not be examined in combination with those two 2+1 modules
Online Offerings
moodle
- Lehrende: Martin Otto
Semester: ST 2023