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This paper aims to give an epistemic interpretation to the tensor disjunctionin dependence logic, through a rather surprising connection to the so-calledweak disjunction in Medvedev's early work on intermediate logic under theBrouwer-Heyting-Kolmogorov (BHK)-interpretation. We expose this connection inthe setting of inquisitive logic with tensor disjunction discussed by Ciardelliand Barbero (2019}, but from an epistemic perspective. More specifically, wetranslate the propositional formulae of inquisitive logic with tensor intomodal formulae in a powerful epistemic language of "knowing how" following theproposal by Wang (2021). We give a complete axiomatization of the logic of ourfull language based on Fine's axiomatization of S5 modal logic withpropositional quantifiers. Finally, we generalize the tensor operator withparameters $k$ and $n$, which intuitively captures the epistemic situation thatone knows $n$ potential answers to $n$ questions and is sure $k$ answers ofthem must be correct. The original tensor disjunction is the special case when$k=1$ and $n=2$. We show that the generalized tensor operators do not increasethe expressive power of our logic, the inquisitive logic, and propositionaldependence logic, though most of these generalized tensors are not uniformlydefinable in these logics, except in our dynamic epistemic logic of knowinghow.

An Epistemic Interpretation of Tensor Disjunction