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

TL;DR

This paper provides a logical framework to analyze different philosophical accounts of knowledge-wh, including mention-some knowledge, false belief sensitivity, and true belief, using bundled operators and axiomatization.

Contribution

It introduces four bundled operators to formalize various knowledge-wh accounts and axiomatizes their corresponding logics within epistemic models.

Findings

Different accounts of knowledge-wh have distinct logical properties.

The four logics exhibit unique reasoning patterns.

The framework clarifies the relationships among knowledge-wh theories.

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: $[\mathsf{tB}^\mathtt{MS}]^x \phi := \exists x (\mathsf{[B]} \phi \wedge \phi)$, $[\mathsf{tB}^\mathtt{MS}_\mathtt{FS}]^x \phi := \exists x (\mathsf{[B]} \phi \wedge \phi) \wedge \forall x (\mathsf{[B]} \phi \to \phi)$, $[\mathsf{K}^\mathtt{MS}]^x \phi := \exists x \mathsf{[K]} \phi$ and $[\mathsf{K}^\mathtt{MS}_\mathtt{FS}]^x \phi := \exists x \mathsf{[K]} \phi \wedge \forall x (\mathsf{[B]} \phi \to \phi)$, 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 $\mathsf{[K]}$) 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.