Abstract

Information exchange can be viewed as a process of asking questions and answering them. While dynamic epistemic logic traditionally focuses on statements, recent developments have been concerned with ways of incorporating questions. One approach, based on the framework of inquisitive semantics, is inquisitive dynamic epistemic logic (textsf {IDEL}). In this system, agents are represented with issues as well as information. On the dynamic level, it can model actions that raise new issues. Compared to other approaches, a limitation of textsf {IDEL} is that it can only encode public announcements. textsf {IDEL} can be refined to encode private questions, by merging its static basis, inquisitive epistemic logic (textsf {IEL}), with action model logic (textsf {AML}). This can be done in two ways, namely by enriching action models with questions as possible actions or with issues concerning which action takes place. This paper describes the corresponding dynamic logics, which are conservative extensions of both textsf {AML} and textsf {IEL}, and a sound and complete axiomatization is given for both.

Highlights

  • Dynamic epistemic logics are used to analyse the process of information exchange: they describe situations in which agents learn facts about the world or about each other’s knowledge

  • As formulas of inquisitive epistemic logic (IEL) are evaluated relative to information states rather than single worlds, the semantics are defined in terms of support rather than truth

  • Let me start by noting that the support relation of Action Model Logic with Questions (AMLQ) has the persistence property and the empty state property, which are the hallmark of inquisitive logics

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Summary

Introduction

Dynamic epistemic logics are used to analyse the process of information exchange: they describe situations in which agents learn facts about the world or about each other’s knowledge. Two prominent approaches are the Dynamic Logic of Questions (DELQ, van Benthem and Minica 2012; Minica 2011) and Inquisitive Dynamic Epistemic Logic (IDEL, Ciardelli and Roelofsen 2015; Ciardelli 2016) These systems are generalizations of Public Announcement Logic (PAL, Plaza 1989): they are used to reason about epistemic events of which all agents are fully aware.. The goal of this paper is to develop an action model variant of IDEL, thereby filling the empty space on the bottom right of the table Doing this amounts to merging the static Inquisitive Epistemic Logic (IEL, Ciardelli and Roelofsen 2015) with AML. A second option is to enrich action models in such a way that they encode issues agents have about which action takes place This is more natural if we think of actions as observations.

Introducing IEL
Modalities and questions
Dynamics
Action model logic
Action models with questions
Action models and logical language
Update procedure
Semantics
Epistemic states and state maps in updated models
Example
Persistence and empty state
Declaratives
Resolutions and normal form
Set modalities and non-deterministic actions
Reduction
Conjunction and inquisitive disjunction
Implication
Knowledge modality
Entertain modality
Axiomatizing AMLQ
Action models with issues
Definitions
Reduction and axiomatization
Comparing AMLQ with AML and IDEL
Simulating AMLQ in AMLI
Combining AMLI with AMLQ
Comparing AMLI with ELQm
Conclusion and further work
Full Text
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