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 doubted 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 φ := \exists x ([B]φ \wedge φ), [tB^MS_FS]^x φ := \exists x ([B]φ \wedge φ) \wedge \forall x ([B]φ \to φ), [K^MS]^x φ := \exists x [K]φ and [K^MS_FS]^x φ := \exists x [K]φ \wedge \forall x ([B]φ \to φ) -, 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.