Timo Eckhardt

Timo Eckhardt (PhD in Philosophy, 2021) ‘Extended Model Semantics and Forgetting in Dynamic Epistemic Logic‘

In this thesis I investigate the idea of modelling epistemic updates as static modal operators. I discuss Extended Model Semantics for Dynamic Epistemic Logics, specifically Action Model Logic with postconditions. I argue that we get a better and more versatile framework for epistemic actions than with the standard update semantics. This comes from the use of normality conditions which act like frame conditions for the modal relationships corresponding to actions. By defining those we pinpoint the exact type of actions we are trying to model and so they give us an easy option to change our actions by simply adding, removing, or changing normality conditions.

Extended models will be used to develop new axiomatic systems. These axioms are non-reductive; i.e., do not simply reduce the truth of dynamic formulas down to the truth of corresponding static epistemic formulas, in nature and, therefore, allow for a better categorisation of epistemic actions mirroring the normality conditions from which they are derived. These axioms will also be used to develop Display Logic proof systems for all logics discussed in the thesis. These are then analysed and shown to be sound and complete and allow for cut-elimination. This has a twofold purpose: it shows the usefulness of normality conditions and the corresponding axioms and it also helps us add to the toolbox of Display Logic as a proof system for modal logic.

I also develop logics of forgetting that allow for modelling of the forgetting of positive epistemic formulas in multi-agent epistemic logic. I also discuss and develop extensions that allow for considering epistemic entrenchment of formulas and the forgetting of negative epistemic formulas and so all epistemic formulas. Additionally, extended semantics for the different logics of forgetting are developed with corresponding non-reductive axioms and, as already mentioned, display calculi.

Supervisors: Professor Greg Restall,  Dr Shawn Standefer