Advanced Logic

URL study guide

https://studiegids.vu.nl/en/courses/2024-2025/X_405048

Course Objective

The objective of the course Advanced Logic is to obtain a basic understanding of modal logic. Knowledge and insight:
- know the Kripke semantics, and variations on that definition, for example game semantics,
- know the tableaux and sequent method for decidability,
- know the notion of bisimulation, and the game approach to (dis)proving bisimularity,
- know the nature of Hilbert style proof systems,
- know basic temporal logic and multi-model logic,
- know propositional dynamic logic and its semantics; Applying knowledge and insight:
- be able to give proofs using Kripke semantics, game semantics,
- be able to decide on (non)validity using the tableaux or sequents method,
- be able to (dis)prove bisimilarity of two pointed models also in a game approach,
- be able to make elementary derivations in Hilbert style systems,
- be able to give proofs and show (non-)bisimilarity for basic temporal logic and multi-modal logic,
- be able to (dis)prove validity and discuss models in propositional dynamic logic; Judgement:
- be able to (dis)prove definability of operators and frame properties in basic modal logic and also in basic temporal logic and multi-modal logic,
- be able to discuss some decidability issues; Communication:
- be able to write elementary proofs; Learning skills:
- have acquired some flexibility in dealing with different versions of modal logic.

Course Content

The course Advanced Logic is concerned with modal logic and its applications to computer science. We study some themes from the book Modal Logics for Open Minds by Johan van Benthem, in particular: basic modal logic and possible world semantics, bisimulation and invariance, modal definability and expressive power, decidability, proof systems, propositional dynamic logic, some epistemic logic.

Teaching Methods

We have two lectures per week, for the duration of seven weeks. Twelve lectures discuss material and two lectures are meant for questions and wrap-up. We have one exercise class per week, for the duration of seven weeks. We discuss (on paper) exercises.

Method of Assessment

There is a written closed-book midterm exam about the first half of the material in week 4 of the course. There is a written closed-book final exam about all material in week 8 of the course. If the grade for the midterm exam is higher than the grade for the final exam, then the midterm counts for 20% of the final grade (midterm-grade + 4*final-exam-grade)/5 ), otherwise the final grade is the grade of the final exam.

Literature

Johan van Benthem, Modal Logics for Open Minds, CSLI Publications 2010. In addition we use slides and exercise sheets.

Target Audience

MSc Artificial IntelligenceMSc Computer ScienceMSc Computer Security

Recommended background knowledge

Basic knowledge of the syntax and semantics of first-order proposition and predicate logic, as for example taught in the Bachelor course Logic and Modelling (X_401015).

Explanation Canvas

We use Canvas for the schedule of the course, and to make available the slides for the lectures and the exercises for the exercise classes. We use Canvas further to provide feedback to the homework assignments, to give the grade for the midterm, and for announcements.