Knowledge-wh and False Belief Sensitivity: A Logical Study (An Extended Abstract)

In epistemic logic, a way to deal with knowledge-wh is to interpret them as a kind of mention-some knowledge (MS-knowledge). But philosophers and linguists have challenged both the sufficiency and necessity of such an account: some argue that knowledge-wh has, in addition to MS-knowledge, also a sensitivity to false belief (FS); others argue that knowledge-wh might only imply mention-some true belief (MS-true belief). In this paper, we offer a logical study for all these different accounts. We apply the technique of bundled operators, and introduce four different bundled operators - [tB(MS)](x) phi := there exists x([B]phi Lambda phi), [tB(FS)(FS)](x) phi :=there exists x([B]phi Lambda phi) Lambda for all x([B]phi up arrow phi), [K-MS](x) phi := there exists x[K]phi and [K-FS(MS)](x)phi :=there exists x[K]phi Lambda for all x([B]phi -> phi) -, which characterize the notions of MS-true belief, MS-true belief with FS, MS-knowledge and MS-knowledge with FS respectively. We axiomatize the four logics which take the above operators (as well as [K]) as primitive modalities on the class of S4:2-constant-domain models, and compare the patterns of reasoning in the obtained logics, in order to show how the four accounts of knowledge-wh differ from each other, as well as what they have in common.