Modal Logics: An Modern Perspective

Contents of the Course

Unit I: Introduction. Introduction (Aims and Evaluation, Methodology). Recap of Propositional and First Order Logic. Basic Modal Logic (Syntax and Semantics). Motivation, Examples, Applications. Other Modal Operators.
Unit II: Modal Logics as Fragments of Classical Logics. The Standard Translation. Transference of Results (Decidability via Translation). Optimized Translations. Automated Reasoning via Translations.
Unit III: Hybrid Logics. Decidable Hybrid Logics (Tableau Calculi). The Down and @ operators and Undecidability. Axiomatizations (Henkin Models). Hybrid XPath (XPath as a query language, Axiomatization, Tableau Calculus).
Unit IV: Description Logics. Web Ontologies and the Semantic Web. Knowledge Bases. A-Box and T-Box Reasoning (Tableau Calculi, Termination).
Unit V: Dynamic Modal Logics. Epistemic Logics (Applications and Limitations). Dynamic Epistemic Logics (Public Announcement Logic, Action Modal Logics, Expressive Power, Decidability). Other Dynamic Modal Operators (Fragments of First Order Logic, Undecidability).

Modal Logics: a semantic perspective. Patrick Blackburn and Johan van Benthem. Handbook of Modal Logics. Elsevier. 2006. [download]
Modal Logic. Patrick Blackburn, Maarten de Rijke and Yde Venema. Cambridge University Press, 2002. Capítulos:
- 1. Basic Concepts. [download]
- 2. Models. [download]
- 3. Frames. [download]
- 4. Completeness. [download]
- 6. Computability and Complexity. [download]
- Bibliography. [download]
First Steps in Modal Logic. Sally Popkorn. Cambridge University Press. 1994. [download]