Group Knowledge And Model Updates Based On Weighted Epistemic Logic

Formal epistemology is not confined to two-valued semantics,and there are growing interests in scalar semantics.Epistemic logicians also realize that knowledge is not an all-or-nothing matter,but sometimes comes in quantitative form.Lots of logics are then proposed,such as graded epistemic logic,probabilistic epistemic logic,and confidence logic in characterizing quantitative knowledge,or beliefs in different applications.Standard epistemic logic is about knowledge with only two values and does not consider different levels of epistemic capabilities that agents might assume.Then,weighted epistemic logic,which is a new kind of quantitative epistemic logic,was proposed by YiN.Wáng et al.,(2021)using the tool of similarity,characterizes agents’ knowledge with restricted epistemic capabilities.However,weighted epistemic logic does not consider group knowledge,and epistemic updates either.In this thesis,I will extend the language of weighted epistemic logic to group knowledge,i.e.,general knowledge,distributed knowledge,and common knowledge.I will introduce three weighted group knowledge modal operators,i.e.,weighted general knowledge operator,weighted distributed knowledge operator,and weighted common knowledge operator,and then analyze the properties of the new operators.The thesis will also discuss two categories of model updates based on weighted epistemic logic,i.e.,public announcements and adjustments of agents’ epistemic capabilities,which come from proactivity or influences from other agents.The dynamic logics in the thesis will reveal how the adjustments of epistemic capabilities influence agents’ epistemic states and deepen the understanding of dynamic epistemic capabilities in weighted epistemic logic.