Barteld Kooi

Dynamic Epistemic Logic

The appendix to the chapter on dynamics supplements the chapter with an overview of dynamic epistemic logic: a branch of logic mainly developed in the decade after the first edition of this handbook was published. Dynamic epistemic logic is an extension of epistemic logic (the logic of knowledge), which focusses on information change, such as communication, usually involving more than one agent. The information of the agents includes information about each others information, socalled higher-order information. The appendix consists of three parts. In the first part an example scenario is presented which can be captured by dynamic epistemic logic. The second part is a historical overview of the main approaches in dynamic epistemic logic is presented. The last part is a look towards the future which attempts to connect ideas from dynamic approaches to language with dynamic epistemic logic.

Dynamic Update with Probabilities

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods.

Probabilistic Dynamic Epistemic Logic

In this paper I combine the dynamic epistemic logic ofGerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The resultis a new probabilistic dynamic epistemic logic, a logic for reasoning aboutprobability, information, and information change that takes higher orderinformation into account. Probabilistic epistemic models are defined, and away to build them for applications is given. Semantics and a proof systemis presented and a number of examples are discussed, including the MontyHall Dilemma.

Expressivity and completeness for public update logics via reduction axioms

In this paper, we present several extensions of epistemic logic with update operators modelling public information change. Next to the well-known public announcement operators, we also study public substitution operators. We prove many of the results regarding expressivity and completeness using so-called reduction axioms. We develop a general method for using reduction axioms and apply it to the logics at hand.

MORAL CONFLICTS BETWEEN GROUPS OF AGENTS

Two groups of agents,

Concurrent Dynamic Epistemic Logic

\mathcal{G}_{1}

Generalized arrow update logic

and

Concurrent dynamic epistemic logic for MAS

{\mathcal{G}}_{2}

Logics of Rational Interaction

, face a moral conflict if

Three-valued Logics in Modal Logic

\mathcal{G}_{1}