Logic of Multi-agent Information Flow

The course is addressed to both MSc students (in Mathematics, CS and MFoCS) and third year undergarduate students (in any of the following fields: Maths, CS, Maths and Comp, MMath, and Maths and Philosophy), with an interest in Logic, AI and the dynamics of information in multi-agent systems. It explores and compares various logical approaches to information flows based on the use of modal logics, on formal languages for the specification of knowledge-related features of a system, and on the use of Kripke models (or transition systems), as abstract models for information systems. A range of important mathematical techniques (such as completeness and decidability proofs, definability and expressivity results etc.) and concepts (bisimulation, canonical models, filtration etc.) are introduced and explained. The course presents applications of these notions to the analysis of information update and communication, and of the role of beliefs and belief-changing actions, in the overall dynamics of any "society" of intelligent agents (e.g. the Internet, the market, communicating networks of robots, cryptographic communication between unreliable or adversary agents over un-secure channels etc.). Implementation of these applications are studied by presenting a range of practical theories of agency in Computer Science and focusing on one of them: the Belief-Desire-Intension (BDI) model that uses modal logic to implement rational agents.

At the end of the course students are expected to:

• Analyze and model interactive scenarios of multi-agent information systems and reason about them using the formal logics (epistemic, dynamic, temporal).
• Work with theoretical aspects of Kripke models of action and information, such as correspondence theory, isomorphism, and bisimulation.
• Model check dynamic properties of information on the presented Kripke models.
• Deduce dynamic properties of information, using the presented proof system.
• Implement rational agents as program specifications, using the dynamic model of information

Week 1. Examples of multi-agent systems and scenarios: NASA Deep Space shuttle, air traffic control,  eBay, Amazon, epistemic puzzles, security protocols

Week 2. Syntax and semantics of multi-modal logics:  Dynamic Logic, Epistemic Logic

Week 3. Applications of the above to reasoning about programs and informative protocols

Week 4. The logic of public and private announcements: Dynamic Epistemic Logic

Week 5. Applications of the above to reasoning about information flow in epistemic puzzles and cryptographic protocols

Week 6. Main theories of agency: Rational (intelligent), Deductive,  Cooperative agents

Weeks 7,8. Implementing rational agents via the Belief-Desire-Intension (BDI) model of  agency

There will be a full set of pdf  slides and  hand outs from the following:

Part 1: Multi-modal logics for multi-agent systems.

• Chapters 1,2,3 of: R. Fagin, J, Halpern, Y. Moses, M. Vardi. Reasoning about Knowledge, MIT Press, 1995.
• Chapter 5 of D. Harel, D. Kozen, J. Tiuryn. Dynamic Logic, The MIT Press, 2000.
• Cahpters 1 to 5 of P. Blackburn, M. de Rijke, Y. Venema. Modal logic, Cambridge University Press, 2001.

Part 2: Dynamic logics of knowledge for information flow in multi-agent systems

• Chapters 4,5,6 of H. van Ditmarsch, W. van der Hoek, B. Kooi. Dynamic Epistemic Logic, Springer, 2007. (The first sections of this book can be used as a concise reference for Part 1.)

Part 3: Implementing multi-agent systems via modal logic

• M. Wooldridge. An Introduction to Multi-agent Systems, John Wiley & Sons, 2002. (slides of a course based on this book are available from http://www.csc.liv.ac.uk/~mjw/pubs/imas/distrib/)