Inquisitive Conditional-Doxastic Logic
Benjamin Sparkes
Abstract:
This thesis develops inquisitive conditional-doxastic logic, obtained by enriching classical multi-agent plausibility models with issues for each agent. The aim of these models is to allow for a finer approach to modelling inquiry.
Issues capture informative and interrogative content, and so by associating an issue to an agent we are able to capture both their information state and their inquisitive state, while a plausibility map on worlds captures their doxastic state. Moreover, inquisitive plausibility models allow for conditionalisation on both informative and interrogative content.
Two conditional-doxastic modalities are introduced and axiomatised; a considers modality unique to inquisitive conditional-doxastic logic, which conditionalises on issues with respect to both an agent’s doxastic and inquisitive state, and a generalisation of (conditional) belief, which conditionalises solely on an agent’s doxastic state.
We show that inquisitive conditional-doxastic logic encodes the same assumptions concerning conditionalisation and conditional-doxastic logic. And, just as conditional-doxastic logic may be taken as the static counterpart to a dynamic logic of belief revision, inquisitive conditional-doxastic logic can be taken as the static counterpart to a dynamic logic of belief revision within an enriched setting that includes formal resources to model interrogatives.
Inquisitive conditional-doxastic logic is shown to be sound and complete with respect to inquisitive plausibility models, and it is shown that both (conditional) belief and knowledge modalities can be defined in terms of the considers modality. However, we also show that the entertains modality of inquisitive epistemic logic cannot be defined by the considers modality. Therefore, as the basic inquisitive conditional-doxastic logic is axiomatised solely by the considers modality over the base inquisitive semantics it cannot be used to reason about an agent’s inquisitive state independently of their doxastic state.
For this reason, we also axiomatise inquisitive plausibility logic and show it is sound and complete with respect to the same class of inquisitive plausibility models. This logic introduces modalities which restrict the issue associated to each agent to the worlds considered at least as plausible as the current world or state of evaluation, and those strictly less plausible. The entertains modality of inquisitive epistemic logic is taken as basic in the axiomatisation of inquisitive plausibility logic, and we show the considers modality of basic inquisitive conditional-doxastic logic is definable. Therefore, inquisitive plausibility logic allows for a full study of the interaction between epistemic and conditional-doxastic modalities within the framework of inquisitive semantics.
Keywords: logic, philosophy