Dynamic epistemic logic

Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (they are called ontic events): for example a red card is painted in blue. They can also bring about changes of knowledge without changing factual properties of the world (they are called epistemic events): for example a card is revealed publicly (or privately) to be red. Originally, DEL focused on epistemic events. We only present in this entry some of the basic ideas of the original DEL framework; more details about DEL in general can be found in the references.

Due to the nature of its object of study and its abstract approach, DEL is related and has applications to numerous research areas, such as computer science (artificial intelligence), philosophy (formal epistemology), economics (game theory) and cognitive science. In computer science, DEL is for example very much related to multi-agent systems, which are systems where multiple intelligent agents interact and exchange information.

As a combination of dynamic logic and epistemic logic, dynamic epistemic logic is a young field of research. It really started in 1989 with Plaza's logic of public announcement.[1] Independently, Gerbrandy and Groeneveld[2] proposed a system dealing moreover with private announcement and that was inspired by the work of Veltman.[3] Another system was proposed by van Ditmarsch whose main inspiration was the Cluedo game.[4] But the most influential and original system was the system proposed by Baltag, Moss and Solecki.[5][6] This system can deal with all the types of situations studied in the works above and its underlying methodology is conceptually grounded. We will present in this entry some of its basic ideas.

Formally, DEL extends ordinary epistemic logic by the inclusion of event models to describe actions, and a product update operator that defines how epistemic models are updated as the consequence of executing actions described through event models. Epistemic logic will first be recalled. Then, actions and events will enter into the picture and we will introduce the DEL framework.[7]

  1. ^ Plaza, Jan (2007-07-26). "Logics of public communications". Synthese. 158 (2): 165–179. doi:10.1007/s11229-007-9168-7. ISSN 0039-7857. S2CID 41619205.
  2. ^ Gerbrandy, Jelle; Groeneveld, Willem (1997-04-01). "Reasoning about Information Change". Journal of Logic, Language and Information. 6 (2): 147–169. doi:10.1023/A:1008222603071. ISSN 0925-8531. S2CID 1700635.
  3. ^ Veltman, Frank (1996-06-01). "Defaults in update semantics". Journal of Philosophical Logic. 25 (3): 221–261. CiteSeerX 10.1.1.77.9349. doi:10.1007/BF00248150. ISSN 0022-3611. S2CID 19377671.
  4. ^ Ditmarsch, Hans P. van (2002-06-01). "Descriptions of Game Actions". Journal of Logic, Language and Information. 11 (3): 349–365. doi:10.1023/A:1015590229647. ISSN 0925-8531. S2CID 195220171.
  5. ^ Cite error: The named reference :0 was invoked but never defined (see the help page).
  6. ^ Baltag, Alexandru; Moss, Lawrence S. (2004-03-01). "Logics for Epistemic Programs". Synthese. 139 (2): 165–224. doi:10.1023/B:SYNT.0000024912.56773.5e. ISSN 0039-7857. S2CID 18793176.
  7. ^ A distinction is sometimes made between events and actions, an action being a specific type of event performed by an agent.