An Inquisitive Dynamic Epistemic Logic with Factual Change

Mellema, René (2019) An Inquisitive Dynamic Epistemic Logic with Factual Change. Master's Thesis / Essay, Artificial Intelligence.

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Abstract

Dynamic Epistemic Logic allows us to model the knowledge that agents have and the effects of actions, such as announcements, on that knowledge. This knowledge also includes various notions of group knowledge, such as common and general knowledge. A good example of such a logic is the Logic of Communication and Change, since it allows us to express various notions of group knowledge in a very natural manner. However, some of the things that it cannot model are the questions that agents have, or the act of asking a question. For this purpose, Inquisitive Semantics was created. Within this field lies the sub-field of Inquisitive Dynamic Epistemic Logic. Inquisitive Dynamic Epistemic Logic is a relatively new field that deals with knowledge, issues that agents have, and epistemic updates to that knowledge and those issues. While the field has shown to be very promising by creating conservative extensions for Epistemic Logic, Public Announcement Logic, and Action Model Logic, it cannot currently model actions with factual change, or (the effects of actions on) common knowledge and public issues. In this thesis we combine these two forms of Dynamic Epistemic Logic into one unified framework. We will do this by first creating an inquisitive epistemic logic of relativized group knowledge, based on Propositional Dynamic Logic (PDL), which we will call Inquisitive Epi- stemic Propositional Dynamic Logic (IE-PDL). We will show that any Inquisitive Epistemic Logic formula can be translated into IE-PDL, and that it is sound and complete with respect to its semantics. This completeness proof differs from the standard construction in Inquisitive Epistemic Logic in that it only works for a finite number of worlds instead of the usual infinite construction. After the creation of IE-PDL, we extend it with action models similar to Action Model Logic with Issues, which results in a logic which we call the Logic of Communication, Change, and Issues (LCCI). Unlike in Action Model Logic with Issues, these action models can also model factual change. We then show that LCCI can be reduced to IE-PDL using the idea of program transformers from the Logic of Communication and Change. We then used this reduction to show that LCCI is sound and complete with respect to finite models and that is is a conservative extension of Action Model Logic with Issues.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Verbrugge, L.C.
Degree programme:	Artificial Intelligence
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	26 Aug 2019
Last Modified:	10 Sep 2019 14:29
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/20776

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